Solving simultaneous equations graphically is the process that allows us to solve two or more algebraic equations that share variables by sketching their graphs. The point (or points) of intersection give(s) the solution(s) to the simultaneous equations.

This is because at the point of intersection the two equations are equal to one another and therefore, the values of the variables are the same for both equations.

Note on how to solve simultaneous equations graphically

1. Identify if the equations are linear or quadratic (or a mix of both)
2. Draw each equation on the same set of axes
3. Find the coordinates where the curves intersect
4. State the values of the variable where the lines intersect and clearly state your answer (if you have multiples values of a variable ensure you match the correct pair)

Example

Using the following graph, find the solutions of the following pairs of equations.