Solve system of linear equations graphically

Question

Solve the following system of equations graphically: y=-x+4 and y=x-2 

Answer

STEP 1:   The given equations represent the equations of lines. We have to find the intercepts of the graph of the given equations and then use them to graph the equations.

First, find the x-intercept of y = –x + 4 by substituting 0 for x.
                                       
Now, replace y with 0 to determine the y-intercept.
The x-intercept is (0, 4) and the y-intercept is (4, 0).

STEP 2:     Plot the intercepts and join them using a straight line to get the graph of y = –x + 4.
STEP 3:    Similarly, we can find the x-intercept and the y-intercept of the graph of the equation y = x – 2.

We get the x-intercept as (0, –2) and the y-intercept as (2, 0).

STEP 4:    Mark the intercepts on the same coordinate plane and join them using a straight line to get the graph of y = x – 2.
STEP 5:    To obtain the solution, find the intersection point of the graphs.
The intersection point is (3, 1).
The solution of the system of equations is thus x = 3 and y = 1.