Question

Which of the following points is a solution to the system of inequalities graphed below?
(graph attatched in comments)


A. (2, 0)
B. (–1, 0)
C. (2, 1)
D. (–3, 2)

Answer 1

@Yuba

Answer 2

I believe the solution is the point of intersection. No?

Answer 3

if it is then you just made this question alot easier.

Answer 4

but that would make it (0,2)

Answer 5

I think either the solutions are wrong or I don't know how to do this question. I'll get back to you.

Answer 6

So the Gray area is our domain of interest.
This area is described by
$$
y \ge 2x+2\\
\implies y-2\ge2x\\
2x\le y-2\\
x\le \cfrac{y-2}{2}\\
y \lt -3x+2\\
\implies y-2\lt -3x\\
-3x > y-2\\
3x\lt 2-y\\
x\lt \cfrac{2-y}{3}
$$
So region is:
$$
x\le \cfrac{y-2}{2}\\
x\lt \cfrac{2-y}{3}
$$
Check that each point satisfies both equations:

A. (2, 0) B. (–1, 0) C. (2, 1) D. (–3, 2)
For example, the 1st point:
$$
2\le \cfrac{0-2}{2}?\\
2\lt \cfrac{2-0}{3}?
$$
The answer is no.

Now check the rest

Answer 7

Does this make sense?

Answer 8

no, i usually just like the answer then i solve it for myself so i can figure out how to do the problem

Answer 9

The guy up there did it right. I forgot this was an inequality. You have to acknowledge your gray area of interest. He basically gave you the answer. All you have to do is sub in the points. One question. How did you find the two equations. I think i get y = 2x+2. But the other one only has one definite point.

Answer 10

as for clynnew, just sub in the points till the statements are true. That is a<=b and a<b for two different equations. Where a and b are two different numbers.

Answer 11

so whats the answer?

Answer 12

<0,2> and <-1,1> looked like good points for the 2nd equation. I used those.

the blue line looked like a dotted line, the red line looks solid

thanks for your questions @OrthodoxMan , glad I could help ya

Answer 13

You pretty much have to solve the inequality clynnew by substituting the 4 points.
Once you find a point that suits the inequality. So for example if 6<=6, then that is correct.
You have to find a point that works for both of them.

Answer 14

i'm going with D

Answer 15

That is your answer!! HOoooraay