Solve the following system of equations by graphing to find the point of intersection. Round to the nearest tenth, if necessary. y = x – 4
y = –9x + 6

a.
(1, –3)
b -1,3
C 3,1
D 3,-1

  a.  (1, -3)

Step-by-step explanation:

A graphing calculator makes short work of solving equations by graphing. The graph and point of intersection are shown in the attached. The solution  is (x, y) = (1, -3).

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Additional comment

It is always a good idea to look at the equations given in the problem.

The equations are in slope-intercept form. This tells you the first equation has a shallow positive slope and a negative y-intercept. It will make a triangle with the axes in the 4th quadrant. The second equation has a steep negative slope and a positive y-intercept. It will make a triangle with the axes in the 1st quadrant.

The x-intercepts in both cases are positive, with the x-intercept of the second equation (2/3) being less than that of the first (4). This tells you the point of intersection cannot be in the first quadrant, but must be in the third quadrant. The x-coordinate of the point of intersection will be between the x-intercept values, closer to the x-intercept of the line with the steep slope. This idea lets you guess that the correct answer will be (1, -3).

step-by-step explanation: