Question

Which of the following points is a solution to the system of linear inequalities?

{y≤2x-5
y>-3x

A.
(1, 1)
B.
(–2, 2)
C.
(5, 3)
D.
(–4, 4)

Answer 1

C. (5, 3)

Explanation:

this point is within the answer area... look below at the graph of both linear inequalities

Answer 2

For this case we have the following system of inequations:

`y\leq2x-5\\y> -3x`

We must replace each of the points and verify that the inequalities are met:

Point A: (1,1)

`1 \leq2 (1) -5\\1 \leq2-5\\1 \leq-3`

It is not fulfilled!

Point B: (-2,2)

`2 \leq2 (-2) -5\\2 \leq-4-5\\2 \leq-9`

It is not fulfilled!

Point C: (5,3)

`3 \leq2 (5) -5\\3 \leq10-5\\3 \leq5`

Is fulfilled!

`3> -3 (5)\\3> -15`

Is fulfilled!

Point D: (-4,4)

`4 \leq2 (-4) -5\\4 \leq -8-5\\4 \leq -13`

It is not fulfilled!

Thus, the point that is the solution of inequalities is:

(5,3)

ANswer:

(5,3)