Solve system of linear equations graphically

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

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.

substituting x with 0

Now, replace y with 0 to determine the y-intercept.

calculating for x

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.

graph of the line 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.

slope and y intercept

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.

graph of the line y=x-2

STEP 5:    To obtain the solution, find the intersection point of the graphs.

the intersection point is (3,1)

The intersection point is (3, 1).
The solution of the system of equations is thus x = 3 and y = 1.

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