Question

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

y < -3x + 3
y < x + 2

(1, -5)

(1, 5)

(5, 1)

(-1, 5)

Answer 1

(1, -5)
-5 < -3(1) + 3
-5 < -3 + 3
-5 < 0
TRUE.
y < x + 2
-5 < 1 + 2
-5 < 3
TRUE.

Answer 2

(1, 5)
5 < -3(1) + 3
5 < -3 + 3
5 < 0
FALSE.
y < x + 2
5 < 1 + 2
5 < 3
FALSE.

Answer 3

is it (1, -5)

Answer 4

(5, 1)
1 < -3(5) + 3
1 < -15 + 3
1 < -12
FALSE.
y < x + 2
1 < 5 + 2
1 < 7
TRUE.

Answer 5

(-1, 5)
5 < -3(-1) + 3
5 < 3 + 3
5 < 6
TRUE.
y < x + 2
5 < -1 + 2
5 < 1
FALSE.

Answer 6

Yes it is (1, -5).

Answer 7

(x, y) = (1, -5)

Answer 8

If you have graphing software or paper you can sketch y = -3x + 3 and y = x + 2 on the same grid. After that you just need to look for the location of the points and see which are less than (below) both lines. This is useful too for when one is below and one is above or when there are more inequalities to compare.