Systems of Equations (Substitution)

Rule

The Substitution Method

1.: Choose one equation and solve for one of the variables.
2.: Put the expression you got in the first step into the equation you haven’t used yet. Solve that equation.
3.: Take this solution and put it back into the first equation. Solve it.
4.: Write the answer as coordinates:
ANSWER: $(x, y) = (a, b)$

Example 1

Solve the system of equations

\begin{array}{l} I1. Choose the equation you think looks easier and solve for one of the variables: \begin{array}{l} I & y + 2 x = 1 \\ y = 1 - 2 x \end{array} 2. Insert the expression you just found into the equation you haven’t used yet: \begin{array}{l} y - x & = - 2 \\ (1 - 2 x) - x & = - 2 \\ 1 - 2 x - x & = - 2 \\ - 3 x & = - 2 - 1 \\ \frac{-3 x}{-3} & = \frac{-3}{-3} \\ x & = 1 \end{array} 3. Then put this value back into the first expression you found: \begin{array}{l} y = 1 - 2 x \\ y = 1 - 2 \cdot (1) \\ y = 1 - 2 \\ y = - 1 \end{array} 4. Write the answer as coordinates: Answer: (x, y) = (1, - 1)Want to know more? Sign Up It's free!Previous entry Systems of Equations (Graphing) Next entry Systems of Equations (Elimination)Home All Math Games Statistics ChatAbout Us About House of Math Employees Career Media Lectures Blog Contact support@houseofmath.com Booking of private tutoring +47 22 150 300 Address Bygdøy allé 23
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            Norway FAQ Links WeTakeAction Math Magic for Ukraine Tutoring Video Crash Courses Junior Math Math Essentials Encyclopedia Language Norsk Українська Terms Privacy{"props":{"pageProps":{"campaign":false,"topic":{"language":"en","breadcrumbs":[{"path":"/drill","h1":"Math Essentials","_key":"09bac112-9008-5368-8dda-35028d5916a1"},{"_key":"0ef35d09-f051-59f2-a098-f18928219db1","path":"/drill/equations","h1":"Equations"},{"path":"/drill/equations/systems-of-equations-substitution","h1":"Systems of Equations (Substitution)","_key":"dcde91db-f1a6-5c78-92ae-8eedfc7aa0be"}],"otherLocales":[],"key":"content/en/drill/08 Equations/18SystemsOfEquationsSub.tex","type":"drill","metaDescription":"The substitution method is another method for solving a system of equations, one of the three methods you need to know to do so efficiently and correctly.","image":null,"siblings":[{"h1":"What Is an Equation?","path":"/drill/equations/what-is-an-equation"},{"h1":"Activities 1","path":"/drill/equations/equations-activities-1"},{"h1":"Remove Number in Front of x","path":"/drill/equations/remove-number-in-front-of-x"},{"h1":"Activities 2","path":"/drill/equations/equations-activities-2"},{"h1":"Remove Number Under x","path":"/drill/equations/remove-number-under-x"},{"h1":"Activities 3","path":"/drill/equations/equations-activities-3"},{"h1":"Equations with Several Terms on Both Sides","path":"/drill/equations/equations-with-several-terms-on-both-sides"},{"h1":"Activities 4","path":"/drill/equations/equations-activities-4"},{"h1":"Equations with Fractions and Parentheses","path":"/drill/equations/equations-with-fractions-and-parentheses"},{"h1":"Activities 5","path":"/drill/equations/equations-activities-5"},{"h1":"Equations with x in the Denominator","path":"/drill/equations/equations-with-x-in-the-denominator"},{"h1":"Activities 6","path":"/drill/equations/equations-activities-6"},{"h1":"Checking the Answer","path":"/drill/equations/checking-the-answer"},{"h1":"Activities 7","path":"/drill/equations/equations-activities-7"},{"h1":"How to Solve Power Equations","path":"/drill/equations/how-to-solve-power-equations"},{"h1":"Activities 8","path":"/drill/equations/equations-activities-8"},{"h1":"Systems of Equations (Graphing)","path":"/drill/equations/systems-of-equations-graphing"},{"h1":"Systems of Equations (Substitution)","path":"/drill/equations/systems-of-equations-substitution"},{"h1":"Systems of Equations (Elimination)","path":"/drill/equations/systems-of-equations-elimination"},{"h1":"Activities 9","path":"/drill/equations/equations-activities-9"},{"h1":"Solutions","path":"/drill/equations/equations-solutions"}],"isRootPath":false,"title":"Systems of Equations (Substitution)","previewUrl":"https://images.houseofmath.com/eyJrZXkiOiJvdmVybGVhZi1hc3NldHMvcHJldmlldy8xOHN5c3RlbXNvZmVxdWF0aW9uc3N1Yi5wbmciLCJidWNrZXQiOiJob20tZnJvbnRlbmQtYXNzZXRzIiwidmVyc2lvbiI6M30=","h1":"Systems of Equations (Substitution)","locale":"en","cssUrl":"/80bd8b3e-74e6-41e8-a473-0237fd221bbf-en-0.css","htmlContent":{"html":" \u003c/p\u003e      \u003cdiv class=\"tcolorbox foorule\" id=\"tcolobox-177\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Rule\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"rule-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eThe\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSubstitution\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eMethod\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e      \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e    1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Choose         one         equation         and         solve         for         one         of         the         variables.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Put         the         expression         you         got         in         the         first         step         into         the         equation         you         haven’t         used         yet.         Solve         that         equation.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     3.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Take         this         solution         and         put         it         back         into         the         first         equation.         Solve         it.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     4.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Write         the         answer         as         coordinates:         \u003cp class=\"noindent\" \u003eANSWER:         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmo  class=\"MathClass-punc\"\u003e,\u003c/mo\u003e\u003cmi  \u003ey\u003c/mi\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi  \u003ea\u003c/mi\u003e\u003cmo  class=\"MathClass-punc\"\u003e,\u003c/mo\u003e\u003cmi  \u003eb\u003c/mi\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e\u003c/math\u003e         \u003c/p\u003e\u003c/dd\u003e\u003c/dl\u003e                                                                                                                      \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-178\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e \u003cp class=\"indent\" \u003e     Example 1\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eSolve the system of equations\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"alignat-star\"\u003e                                   \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-even\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003eI\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\" class=\"qquad\"/\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                             \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-even\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmphantom\u003e  \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003c/mphantom\u003e \u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e                                   \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-even\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003eI\u003c/mi\u003e\u003cmi  \u003eI\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\" class=\"qquad\"/\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                            \u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-even\"\u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmphantom\u003e  \u003cmn\u003e2\u003c/mn\u003e \u003c/mphantom\u003e \u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cp class=\"noindent\" \u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eusing the substitution method\u003c/span\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e\u003c/b\u003e\u003c/p\u003e                                                                                               \u003cdiv class=\"lowerbox\"\u003e                                                                                                                                                                                                                                           \u003cp class=\"noindent\" \u003e         \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eChoose the equation you think looks easier and solve for one of the variables:         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                             \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003eI\u003c/mi\u003e\u003cmspace width=\"1em\" class=\"quad\"/\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-label\"\u003e                                             \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmstyle mathcolor=\"#E60000\"\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eInsert the expression you just found into the equation you haven’t used yet:         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                       \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmstyle mathcolor=\"#E60000\"\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                              \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e2\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmfrac\u003e\u003cmrow  \u003e\u003cmtext class=\"cancel\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtext\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mrow\u003e  \u003cmrow  \u003e\u003cmtext class=\"cancel\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtext\u003e\u003c/mrow\u003e\u003c/mfrac\u003e \u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmfrac\u003e\u003cmrow  \u003e\u003cmtext class=\"cancel\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtext\u003e\u003c/mrow\u003e  \u003cmrow  \u003e\u003cmtext class=\"cancel\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtext\u003e\u003c/mrow\u003e\u003c/mfrac\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e                                       \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmstyle mathcolor=\"#E60000\"\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                      \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     3.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eThen put this value back into the first expression you found:         \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                             \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e                                    \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e⋅\u003c/mo\u003e \u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmstyle mathcolor=\"#E60000\"\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-label\"\u003e                                             \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-label\"\u003e                                             \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-even\"\u003e\u003cmi  \u003ey\u003c/mi\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     4.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003eWrite the answer as coordinates: \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle  class=\"text\"\u003e\u003cmtext  \u003eAnswer: \u003c/mtext\u003e\u003c/mstyle\u003e\u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmo  class=\"MathClass-punc\"\u003e,\u003c/mo\u003e\u003cmspace width=\"0.22em\" class=\"thinspace\"/\u003e\u003cmi  \u003ey\u003c/mi\u003e\u003cmo  class=\"MathClass-close\" stretchy=\"false\"\u003e)\u003c/mo\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-open\" stretchy=\"false\"\u003e(\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmo  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