How to Solve Systems of Equations in GeoGebra

You can use GeoGebra to solve systems of equations.

GeoGebra Instruction 1

Solution in `CAS`

1.: Open CAS under View in Menu.
2.: Enter your equations one by one in CAS, pressing Enter to start a new row for each of your equations.
3.: Select each of the rows with an equation in them by clicking the boxes with a row number. You’ll know that the row is selected when the box with the row number has turned purple. To select more than one box at a time, hold down the Shift key, click the box of the first equation and then click the box with the row number of the last equation.
4.: Click Solve .

If you get ${}$ as the output, the system of equations has no solution. If GeoGebra returns one of the variables as a function, the system of equations has infinitely many solutions.

Screenshot of GeoGebra showing the simultaneous solution of two equations

You can solve a system of equations graphically by plotting all the graphs in the same coordinate system. The solutions are intersections between the graphs.

GeoGebra Instruction 2

Solution in `Graphics View`

1.: Open Algebra View and Graphics View under View in Menu.
2.: Enter your equations one by one in CAS, pressing Enter to start a new row for each.
3.: In Toolbar, click Intersect . If you can’t find the button, check that you have the Toolbar for Graphics View by clicking on any empty space inside the Graphics View window. Then find the button under the Point tool list.
4.: Click the graphs in Graphics View. The order does not matter.
5.: The solutions are given in Algebra View as coordinates of the intersection points.

Screenshot of GeoGebra showing the intersection of two lines

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Solution in CAS

Solution in Graphics View

Solution in `CAS`

Solution in `Graphics View`