# Solving Systems of Equations by Graphing

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System of equations are the set of linear equations consisting of different variables and constants arranged together. Solving system of equations involves finding the values of the variables given in the equations. System of equations can be solved using different methods and one of such methods is by graphing. In graphing, the given equations are graphed on a coordinate plane and the point where the straight lines intersect, that point gives the value of the variables. If there is no point of intersection between the lines, then there is no solution.

Example 1: Solve the system of equations, y = x and y = 2x by graphing.

To graph the equations, we need get their coordinate points.

This means for y = x, the coordinate points can be (0, 0), (1, 1), (-1, -1), (2, 2).

Similarly for y = 2x, the coordinate points can be (0, 0), (1, 2), (-1, -2), (2, 4).

When the coordinate points are plotted on the graph, they have the common point (0, 0) which is their point of intersection.

Hence the solution of the equations is x =0 and y = 0.

Example 2:Solve the system of equations, y = x and y = 3x - 2 by graphing.

This means for y = x, the coordinate points can be (0, 0), (1, 1), (-1, -1), (2, 2).

Similarly for y = 3x - 2, the coordinate points can be (0, -2), (1, 1), (-1, -5), (2, 4).

When the coordinate points are plotted on the graph, they have the common point (1, 1) which is their point of intersection.

Hence the solution of the equations is x =1 and y = 1.