Question

Choose the system of inequalities that matches the graph below.

Choices:

A.y ≥ x + 3
y ≤ x – 2

B.y > x + 3
y < x – 2

C.y ≤ x + 3
y ≤ x – 2

D.y ≤ x + 3
y ≥x – 2

Answer 1

So the solution to the system is the green area. You can see that the green area is under the line that has positive slope, and above the line that has negative slope. That should help eliminate a few options.

Answer 2

so i shud eliminate A and C?

Answer 3

You can definitely eliminate A and C. For the reason I stated above.

Answer 4

What about D

Answer 5

What is the sign of the slopes of those lines?

Answer 6

less than or equal to and greater than or equal to?

Answer 7

No but the slope:

y = x + 3 has a positive or a negative slope?
y = x - 2 has a positive or a negative slope?

Answer 8

positive and negative

Answer 9

No, they both have positive slope.

Answer 10

The coefficient on the x variable is positive.

Answer 11

oh

Answer 12

But looking at your graph, one of the lines has a negative slope (goes down as you move right). Therefore it cannot be D.

Answer 13

And poof. We found the answer without even having to solve the system.

Answer 14

This is why giving people multiple choice is silly in math. Far too easy to eliminate wrong solutions so you don't have to actually find the right one.

Answer 15

Yeah it's kind of confusing, thanks for the help! :)