Question

Which of the following ordered pairs (x,y) satisfies both the inequalities y ≥ 3x +8 and y < x?

E. (2,1)
F. (2,-1)
G. (8,-1)
H. (-8,-9

Answer 1

The answer would be H -8 -9

Answer 2

H. (-8,-9)

Explanation:

Our inequalities:

y ≥ 3x + 8

y < x

To find which ordered pair satisfies both inequalities, we have to plug in values for x and y.

Option E:

y ≥ 3x + 8
y < x

(1) ≥ 3(2) + 8
=1 ≥ 14
(1) < (2)

As we can see, the first inequality is a false statement. So option E is incorrect.

Option F:

y ≥ 3x + 8
y < x

(-1) ≥ 3(2) + 8
=-1 ≥ 14
(-1) < (2)

The first inequality is also a false statement, so this option is also incorrect.

Option G:

y ≥ 3x + 8
y < x

(-1) ≥ 3(8) + 8
-1 ≥ 32
-1 < 8

The first inequality is a false one, so option G is incorrect.

Option H:

y ≥ 3x + 8
y < x

-9 ≥ 3(-8) + 8
-9 ≥ -16
-9 < -8

The first inequality and second inequality are both true. This makes option H the correct one.

Hope this helps! :)