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

(1, −10)

Explanation:

If we graph this system of inequalities, we could find the solution.

From the graph you can deduct that the only right answer is the last one (1,-10), because the area of solution is only for negative values of y.

Therefore, the right choice is the last one.

If you can't graph, you can try another method. If we replace the value in the system, it should satisfy it, that is, it should gives us a true result like 0<1 for example. Let's try

For x=1 and y=-10, we have

-10 ≤ 1 − 5

-10 ≤ −1 − 4

-10 ≤ -4

-10 ≤ -5

As you can see, the result is true, because -10 is less than -4 and -5, so that's the right answer.

Answer 2

Explanation:

y ≤ x − 5

1<10-5

1<5

Pair: (10,1)

y ≤ −x − 4

-10<-1-5

-10<-6

Pair: (1,-10)