# How do you graph and check to solve a linear system of equations in two variables?

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Let given system of equations be

2x+y=5

x+2y=4

First form tables for both equation as ie find points (minimum three)

by assiging different values of x ,getting values of y.

y=5-2x

(0,5),(1,3),(2,1)

Plot its graph , similarly repeat same process for another equation.If graph of the equations intersect ,the point of the intersection be the solution of the system of equation.

If lines do not intersect ,they are parallel then either no solution or infinite no. of solutions.

graph ,for considered example

Red and green lines intersect each other at x=2 ,y=1 .Thus solution of the problem is

x=2,y=1

Let consider another example.

x+y=4

2x+2y=3

Lines are parallel , so no solution.

another example

x+y=2

2x+2y=4

Both equations have same graph. so infinite no. of solutions.

Substitute the values of x and y ,to verify your answer.