Question

Which ordered pair makes both inequalities true? y > –3x + 3 y > 2x – 2 On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (1, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 3) and (1, 0). Everything to the right of the line is shaded. (1,0) (–1,1) (2,2) (0,3)

Answer 1

Answer: (4,0)

Step-by-step explanation: I took the test!

Answer 2

Answer:

None of the points (1,0), (-1,1), (2,2) and (0,3) makes both inequalities true

Step-by-step explanation:

You are given two inequalities:

$y>-3x+3$

and

$y>2x-2$

The attached diagram shows the common set of points which coordinates suit two inequalities.

As you can see all points (1,0), (-1,1), (2,2) and (0,3) do not belong to the common region (only to one of them or even do not belong to both of them)

You can check it analitically:

(1,0):

$0>-3\cdot 1+3=0\ \text{False}\\ \\0>2\cdot 1-2=0\ \text{False}$

(-1,1):

$1>-3\cdot (-1)+3=6\ \text{False}\\ \\1>2\cdot (-1)-2=-4\ \text{True}$

(2,2):

$2>-3\cdot 2+3=-3\ \text{True}\\ \\2>2\cdot 2-2=2\ \text{False}$

(0,3):

$3>-3\cdot 0+3=3\ \text{False}\\ \\3>2\cdot 0-2=-2\ \text{True}$