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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)

Respuesta :

calculista

Answer:

(4,0)

Step-by-step explanation:

we have

[tex]y< 3x-1[/tex] ----> inequality A

[tex]y \geq -x+4[/tex] ----> inequality B

we know that

If a ordered pair is a solution of 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

[tex]0< 3(4)-1[/tex]

[tex]0< 11[/tex] ----> is true

Inequality B

[tex]0 \geq -(4)+4[/tex]

[tex]0 \geq 0[/tex] ----> is true

so

the ordered pair makes both inequalities true

case 2) (1,2)

Inequality A

[tex]2< 3(1)-1[/tex]

[tex]2< 2[/tex] ----> is not true

so

the ordered pair not makes both inequalities true

case 3) (0,4)

Inequality A

[tex]4< 3(0)-1[/tex]

[tex]4< -1[/tex] ----> is not true

so

the ordered pair not makes both inequalities true

case 4) (2,1)

Inequality A

[tex]1< 3(2)-1[/tex]

[tex]1< 5[/tex] ----> is true

Inequality B

[tex]1 \geq -(2)+4[/tex]

[tex]1 \geq 2[/tex] ----> is not true

so

the ordered pair not makes both inequalities true

Answer:

the answer is (4,0)

Step-by-step explanation:

It is (4,0) because it is on the solid line.:)

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