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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 xx- and yy-values where the graphs intersect each other. Let us say that you have the following system of equations: {2y=62xx=y1.\begin{cases}2y=6-2x \\ x=y-1. \end{cases} You need to find the pair of xx- and yy-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 = mmx + cc, by solving for yy on the left hand side. {y=3xy=x+1.\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).(1,2). The solution for the simultaneous equations is therefore {x=1y=2.\begin{cases}x=1 \\ y=2. \end{cases}

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