Let given system of equations be
First form tables for both equation as ie find points (minimum three)
by assiging different values of x ,getting values of y.
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
Let consider another example.
Lines are parallel , so no solution.
Both equations have same graph. so infinite no. of solutions.
Substitute the values of x and y ,to verify your answer.