Question

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

y less than or greater to x - 5
y less than or greater to -x - 4

Choices:

(1, 10)
(-1, 10)
(10, 1)
(1, -10)

Answer 1

you can graph both equation and can find solution where both lines intersect that point is your solution

Answer 2

https://www.desmos.com/calculator
use this to graph and let me know if you wanna do other method

Answer 3

Take each point (x,y) and put in the numbers, which one makes both equations true?

Answer 4

For example (1,10)\[10 \le 1 - 5\]
\[10 \le -1 - 4\]

Those are false, so that point is not in the solution set for those 2 inequalities. I am assuming you mean 'less than or equal too' in the problem.

Answer 5

Yes that is what I meant

Answer 6

Try the second point out (x,y) = (-1,10)

Answer 7

From the first inequality , using this point you can see this one is also false

10 is less than or equal to -1-5 nope

Answer 8

i guess there is a typo less than or equal to**
less than or equal** to

Answer 9

yes, that is what it should be , he said above

Answer 10

or she

Answer 11

What do you get using the third point?

Answer 12

I am confused though on how to do it

Answer 13

\[y \le x - 5\]

third point is (10 , 1), in there x = 10, y = 1
Put that into the above inequality , and see if it is true or false

Answer 14

\[1 \le 10 - 5 ~~~;~~1 \le 5\] That is true, now try it in the second inequality

Answer 15

\[y \le -x - 4 ~~~~;~~~~1 \le -10-4 \] that is false, so the point (10,1) is not in the solution set,

the point has to satisfy both of the inequalities to be part of the solution set

Answer 16

u see what i am doing, just putting the x and y values into the inequality, and seeing if it is true or false?

last one says, 1 is less than or equal to negative 14, that is false

Answer 17

that leaves just the 4h point to test, and since the others were all false, the last point in the list should be true and be part of the solution set

Answer 18

another approach is to set the y equal and solve for x

Answer 19

also correct the question before checking the inequality