Question

How do you solve linear equations by graphical method$?$

Answer 1

Solving linear equation by graphical method:

The procedure of solving a system of linear equations by drawing the graph is known as the graphical method.

To solve a pair of linear equations in two variables graphically we follow the following steps:

Step 1. Get the given system of linear equations in two variables.

Step 2. Plot the graph of the first equation and then the second equation on the same coordinate system.

The following three cases may arise by plotting the graphs:

Case 1. If the line intersect at a point, then the given system has a unique solution given by the coordinates of the point of intersection.

Case 2. If the lines are coinciding, then the system is consistent and has infinitely many solutions.

Case 3. If the lines are parallel, then the given system of equations is inconsistent that is it has no solution.

Now, let us solve the system of linear equations by the graphical method.

Consider two linear equations,

$y=x-1$

$y=2x+2$

Now, graph the equations in the coordinate plane.

From the graph, we can see the two linear equations intersect at the common point $(-3,-4)$, which is the solution for the given system of linear equations.

Hence, we can solve linear equations by plotting the graph on coordinate system in graphical method.