Solve system of linear equations graphically
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.