Question

Which of the following points lie in the solution set to the following system of inequalities?

y > -3x + 3
y > x + 2

(2, -5)

(-2, 5)

(2, 5)

(-2, -5)

Answer 1

Did you try graphing the system?

Answer 2

No. @e.mccormick

Answer 3

Well, you can solve this by graphing it and seeing what would fall in the overlap. OR, you can try the x and y values from each and see if they are true for both equations.

Answer 4

How do I do that?

Answer 5

Graphing it? Well, you graph the line it would be on, then shade the proper side based on the >.

Trying things? For \((2, -5)\)
\(y > -3x + 3 \implies -5 > -3(2) + 3 \)
If that is false, skip to the next possible answer. But if it is true, then try:
\(y > x + 2 \implies -5 > 2 + 2 \)

If you knw the graphing, the first is easy. But if you are not sure on the graphing, the second will work and is simple to do.

Answer 6

I'm not sure what you did here.

Trying things? For (2,−5)
y>−3x+3⟹−5>−3(2)+3
If that is false, skip to the next possible answer. But if it is true, then try:
y>x+2⟹−5>2+2

Answer 7

I put in the x and y.

Answer 8

What does that mean?

Answer 9

The answer are in the form of ordered pairs: \((x,y)\). So \((2, -5)\) means `Use 2 for x` and `Use -5 for y`. So I put those into the equations.

Answer 10

Thank you.

Answer 11

FYI: \(\implies\) means implies. It is a a way of saying, "This can become that." in math. Another one you may see is \(\therefore\), which means therefore.

\((2, -5)\) means x is 2, y is 5. Therefore:
\(y > -3x + 3 \implies -5 > -3(2) + 3 \)

So I simplify that:
\(-5 > -3(2) + 3 \implies -5 > -6 + 3 \)

\( -5 > -6 + 3 \implies -5 > -3 \)

That is FALSE! So I do not need to do any more and that answer is bad. But, just to see, lie me work the other equation anyway.

\(y > x + 2 \implies -5 > 2 + 2 \)

\( 5 > 2 + 2 \implies -5 > 4 \)

That is also false. So answer A has nothing good about it!

You should be able to go on from there. Have fun!