Question

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

y ≤ x − 5
y ≤ −x − 4
(1, 10)
(−1, 10)
(10, 1)
(1, −10)

Answer 1

I think the answer is (1, −10) hope this helps

Answer 2

(1, -10)

Explanation:

Since, a point lies in the solution set to a system of inequalities if it satisfies all inequalities of the system.

Here, the given system of inequalities,

y ≤ x - 5

y ≤ -x - 4,

Since, for (1, 10),

10 ≤ 1 - 5 ( False ),

⇒ (1, 10) does not lie in the solution of the system,

For (-1, 10),

10 ≤ -1 - 5 ( False ),

⇒ (-1, 10) does not lie in the solution of the system,

For (10, 1),

1 ≤ -10 - 4 ( False ),

⇒ (10, 1) does not lie in the solution of the system,

For (1, -10),

-10 ≤ 1 - 5 ( True )

-10 ≤ -1 - 4 ( True ),

⇒ (1, -10) lies in the solution of the system.