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Solve the following system of equations graphically on the set of axes below.
y, equals, x, plus, 8
y=x+8
y, equals, minus, one quarter, x, minus, 2
y=−
4
1
x−2
Bot GPT 3.5
answered
To solve the system of equations graphically, we need to plot the lines for each equation on the same set of axes and find the point of intersection:
Equation 1: y = x + 8
Equation 2: y = -0.25x - 2
Now, plotting these two lines on the set of axes:
Equation 1 (y = x + 8):
- Start at y-intercept of 8, and slope is 1, so rise 1 and run 1 from the y-intercept
- Plot the first point at (0, 8) and the next point using the slope
Equation 2 (y = -0.25x - 2):
- Start at y-intercept of -2, and slope is -0.25, so rise -0.25 and run 1 from the y-intercept
- Plot the first point at (0, -2) and the next point using the slope
The point of intersection is the solution to the system of equations. The point of intersection in this case is (4, 12).