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# Graphical Solutions - Simultaneous Equations

A graphical solution for a system of equation means drawing the equations as graphs and determining the $x$- and $y$-values where the graphs intersect each other. Let us say that you have the following system of equations: $\begin{cases}2y=6-2x \\ x=y-1. \end{cases}$ You need to find the pair of $x$- and $y$-values that solve both equations at the same time. This occurs where the lines intercept each other.

Begin by rewriting the equations in the slope-intercept form, y = $m$x + $c$, by solving for $y$ on the left hand side. $\begin{cases}y=3-x \\ y=x+1. \end{cases}$

You can either draw the functions by hand or by using a graphing calculator.

Now you can find the point of intersection.

The graphs intersect each other at the point $(1,2).$ The solution for the simultaneous equations is therefore $\begin{cases}x=1 \\ y=2. \end{cases}$

Often, it is practical to use a calculator to work with graphic solutions.