Question

Which ordered pair makes both inequalities true?

y < 3x – 1

y > –x + 4

On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (0, negative 1) and (1, 2). Everything to the right of the line is shaded. The second solid line has a negative slope and goes through (0, 4) and (4, 0). Everything above the line is shaded.
(4,0)
(1,2)
(0,4)
(2,1)

Answer 1

The ordered pair that makes both inequalities true is (4,0).

we have

y<3x-1 ----> inequality A

y > –x + 4----> inequality B

we know that

If an ordered pair is a solution to the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each ordered pair

case 1) (4,0)

Inequality A

0<3(4)-1 ----> is true

Inequality B

0> –4 + 4 ----> is true

What is inequality?

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

So, The ordered pair makes both inequalities true

case 2) (1,2)

Inequality A

2< 3(1) – 1

2<3-1

2<2----> is not true

So the ordered pair does not make both inequalities true

case 3) (0,4)

Inequality A

0 < 3(4) – 1

0<12-1

0<11 ----> is not true

So, the ordered pair does not make both inequalities true

case 4) (2,1)

Inequality A

1< 3(2) – 1

1<6-1

1<5----> is true

Inequality B

$1\geq -2+4$

$1\geq 2$ ----> is not true

So the ordered pair does not make both inequalities true.

To learn more about the inequalities visit:

https://brainly.com/question/24372553

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