Colorful House of Math logo
Log in

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 I y + 2x = 1 II y 2 x = 2

using the substitution method

1.
Choose the equation you think looks easier and solve for one of the variables: I y + 2x = 1 y = 1 2x
2.
Insert the expression you just found into the equation you haven’t used yet: y x = 2 (1 2x) x = 2 1 2x x = 2 3x = 2 1 3x 3 = 3 3 x = 1
3.
Then put this value back into the first expression you found: y = 1 2x y = 1 2 (1) y = 1 2 y = 1
4.
Write the answer as coordinates: Answer: (x,y) = (1, 1)

Want to know more?Sign UpIt's free!
White arrow pointing to the LeftPrevious entry
Systems of Equations (Graphing)
Next entryWhite arrow pointing to the right
Systems of Equations (Elimination)