Question

Solve this system by graphing.

y = 2x - 7
y = - 3x + 8


(3, -1)


(4, 1)


(0, 8)


(0, -7)

Answer 1

(a) (3, -1)

Explanation:

You want the graphical solution to the system ...

• y = 2x -7
• y = -3x +8

Graph

A graphing calculator plots these equations easily, and will give you the coordinates of the point where the lines intersect. That point is the solution to the system of equations:

(x, y) = (3, -1)

__

Additional comment

Here, the offered choices are the y-intercepts (clearly wrong), and points in the first and fourth quadrants. You can choose the correct point by thinking about the x-intercepts.

The line with positive slope has an x-intercept of 7/2 = 3.5. For positive x-values less than this, the line is in the 4th quadrant.

The line with negative slope has an x-intercept of -8/-3 ≈ 2.7. For positive x-values greater than this, the line will be in the 4th quadrant.

The point of intersection must be in the 4th quadrant with an x-value between 2.7 and 3.5. Only one answer choice is like this: (3, -1).