Question

Solve the following system by graphing and identify the point of intersection.

-2x-y=-12
2x-3y=4

O (2,5)
O (5,2)
O (-5,-2)
O (-2,-5)

Answer 1

(b) (5, 2)

Explanation:

You want the point of intersection of the lines defined by ...

• -2x -y = -12
• 2x -3y = 4

Graph

The attachment shows a graphical solution to the system of equations.

The point of intersection is (5, 2), choice B.

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Additional comment

It is convenient to graph the first equation using its intercepts. The x-intercept is the solution with y=0:

-2x = -12 ⇒ x = 6

The y-intercept is the solution with x=0:

-y = -12 ⇒ y = 12

The line through these intercept points is the red line in the attachment.

The second equation has an x-intercept easy to find and graph:

2x = 4 ⇒ x = 2

The y-intercept is negative (-4/3), so the line will have an upward slope at x=2. It must cross the first line between x=2 and x=6, eliminating all answer choices except the correct one.

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