Question

Which of the following points lie in the solution set to the following system of inequalities? (1 point)

y ≤ x − 5
y ≤ −x − 4

(1, 10)
(1, −10)
(10, 1)
(−1, 10)

Answer 1

the solution is the point
`(1,-10)`

Explanation:

we have

`y\leq x-5` -------> inequality A

`y\leq -x-4` -------> inequality B

The solution of the system of inequalities is the shaded area

see the attached figure

We know that

If a point is a solution of the system of inequalities

then

the point must be on the shaded area of the solution of the system of inequalities

so

Plot the points and verify if they are on the shaded area

the solution is the point
`(1,-10)`

Answer 2

(1,-10)
the 10 must be negative

reason why the others dont work:
(1,10) too positive, the other two start negative, no way is it going to be way up here
(10,1) still too high
(-1,10) then again, too high