Mr. Coleman is mapping the boundaries of a zoo on a coordinate grid. The zoo’s headquarters are located at the origin. The equations shown below represent two boundaries of the zoo.

Question

y = −2x – 5
−2x + 4y = 12

Answer 1

To find the coordinate points where the boundaries intersect, we can set the two equations equal to each other:

-2x - 5 = -2x + 4y = 12.

Next, we solve for y:

-2x - 5 = 12
4y = 12
y = 17

Now that we have the y-coordinate, we can solve for the x-coordinate by substituting y back into one of the original equations:

y = -2x - 5
17 = -2x - 5
2x = -22
x = -11

Therefore, the boundaries intersect at the point (-11, 17). This point represents a corner of the zoo's boundary on the coordinate grid.