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System of equations
Solving systems of equations by graphing

Solving systems of equations by graphing is one method to find the point that is a solution to both original equations.

With this method you first sketch the lines representing the two equations. Then you try to determine whether the two lines intesect at a point. That is:

1. Graph both equations, obtaining two straight lines.
2. The simultaneous solution is given by the coordinates (x,y) of the point of intersection of these lines.

Solve by graphing: $\left{2y-x=4\\x+y=5$
1. Write each equation in slope-intercept form:

$y=\frac{1}{2}x+2\;\;\;\;$$y=5-x$

2. Graph both equations:

The graphs intersect at the point (2,3), so (2,3) is the solution of the system.

Solve by graphing:

 $\left{9x+2y=-48\\-4x+6y=42$ x= y=