Question

Which ordered pair makes both inequalities true?

Answer 1

Answer:

The ordered pair $(-1,1)$ make both inequalities true

Step-by-step explanation:

we have

$y$ ------> inequality A

$y > 2x-2$ ------> inequality B

we know that

If a ordered pair satisfy both inequalities

then

the ordered pair is a solution of both inequalities

we're going to verify every case

case A) point $(1,0)$

Substitute the values of x and y in both inequalities

$x=1, y=0$

Inequality A

$y$

$0$

$0 < 0$ ------> is not true

therefore

The ordered pair $(1,0)$ does not make both inequalities true

It's not necessary to verify the B inequality

case B) point $(-1,1)$

Substitute the values of x and y in both inequalities

$x=-1, y=1$

Inequality A

$y$

$1$

$0 < 6$ ------> is true

Inequality B

$y > 2x-2$

$1 > 2*(-1)-2$

$1 > -4$ ------> is true

therefore

The ordered pair $(-1,1)$ make both inequalities true

case C) point $(2,2)$

Substitute the values of x and y in both inequalities

$x=2, y=2$

Inequality A

$y$

$2$

$2 < -3$ ------> is not true

therefore

The ordered pair $(2,2)$ does not make both inequalities true

It's not necessary to verify the B inequality

case D) point $(0,3)$

Substitute the values of x and y in both inequalities

$x=0, y=3$

Inequality A

$y$

$3$

$3 < 3$ ------> is not true

therefore

The ordered pair  $(0,3)$ does not make both inequalities true

It's not necessary to verify the B inequality

Answer 2

Answer:

(2,2).

Step-by-step explanation:

The given inequalities are

$y>-3x+3$

$y>2x-2$

To answer this question, we just have to replace each pair and see which one makes these inequalities true.

For $(1,0)$

$y>-3x+3\\0>-3(1)+3\\0>-3+3\\0>0$

$y>2x-2\\0>2(1)-2\\0>2-2\\0>0$

For $(-1,1)$

$y>-3x+3\\1>-3(-1)+3\\1>3+3\\1>6$

$y>2x-2\\1>2(-1)-2\\1>-2-2\\1>-4$

For $(2,2)$

$y>-3x+3\\2>-3(2)+3\\2>-6+3\\2>-3$

$y>2x-2\\2>2(2)-2\\2>4-2\\2>2$

For $(0,3)$

$y>-3x+3\\3>-3(0)+3\\3>3$

$y>2x-2\\3>2(0)-2\\3>-2$

Now, if we graph, we could get the right answer, because with these results the answer is not clear.

In the graph, you could see that (2,2) (1,0) and (0,3) could answers here, because all three of them present the same characteristic, they are in the edge of the shaded area.

However, when we have inequality system problems, those which have a null coordinate don't apply for solution.

Therefore, the best answer is (2,2).