Question

Which point lies in the solution set for the following system of inequalities?

2x + y < 4
x - y > 3
Answer
(2, -3)
(5, -2)
(3, 4)
(0, 0)

Answer 1

I'm just curious.

Why not compute it yourself? Put the points in. See if they work.

Answer 2

i did n they all come out to be false so i might doing something wrong but idk

Answer 3

Ok. (0,0) doesn't work. You can tell that immediately. To check if a point \((x_1,y_2)\) works, just put it in like this: \(2x_1+y_1<4\) and \(x_1-y_1>3\). Here's an example: To test \((8,9)\) we do this:
\[
\begin{align}
2(8)+(9)&<4\\
16+9&<4\\
25&<4
\end{align}
\]
Since \(25\) is not less than \(4\), the point \((8,9)\) does not work. Try the other points just like this. If they work for one inequality, check the other. If they work for both, then that's the point you pick. :D

Answer 4

haha i got it thanks :)

Answer 5

YAAAAYYYYYYYY WOOOHOO :D

Answer 6

lol :p

Answer 7

you can try making the graph for better understanding

Answer 8

^this, too, helps.. unless you're as lazy as I am.

Answer 9

Heck, I visualize them more often than I do actually graph them..

Answer 10

i did that graph thing and i got it the same thing as i did when i plugged in the numbers

Answer 11

You are supposed to. They represent the same thing.

Answer 12

yeaa ik i get what i was doing wrong