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Nadya [2.5K]
3 years ago
5

Which ordered pairs make both inequalities true? Check all that apply.

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0
All others did not satisfy the inequality simultaneously except #4 and #6
For #4:
2 < 5(1) + 2 i.e. 2 < 7 (true)
2 >= 1/2(1) + 1 i.e. 2 >= 3/2  (true)
For #6
2 < 5(2) + 2 i.e. 2 < 12 (true)
2 >= 1/2(2) + 1 i.e. 2 >= 2

Ganezh [65]3 years ago
6 0

we have

y < 5x + 2 -------> inequality 1y \geq \frac{1}{2}x + 1 -------> inequality 2

using a graph tool

see the the attached figure N 1

the solution of the system is the shaded area

case 1) (-3, 2)

This point satisfies the inequality 2 but does not satisfy the inequality 1.

therefore

it is not a solution of the system

see the attached figure N 2


inequality 1

(-3,2)\\ x=-3\\ y=2

2 < 5*(-3) + 2

2 < -13 -----> is not true

inequality 2

(-3,2)\\ x=-3\\ y=2

2 \geq \frac{1}{2}*(-3) + 1

2 \geq -\frac{1}{2} -----> is true

case 2) (-1, 3)

This point satisfies the inequality 2 but does not satisfy the inequality 1.

therefore

it is not a solution of the system

see the attached figure N 2


inequality 1

(-1, 3)\\ x=-1\\ y=3

3 < 5*(-1) + 2

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

inequality 2

(-1, 3)\\ x=-1\\ y=3

3 \geq \frac{1}{2}*(-1) + 1

3 \geq \frac{1}{2} -----> is true

case 3) (0, 2)

This point satisfies the inequality 2 but does not satisfy the inequality 1.

therefore

it is not a solution of the system

see the attached figure N 2


inequality 1

(0, 2)\\ x=0\\ y=2

2 < 5*(0) + 2

2 < 2 -----> is not true

inequality 2

(0, 2)\\ x=0\\ y=2

2 \geq \frac{1}{2}*(0) + 1

2 \geq 1 -----> is true

case 4) (1, 2)

This point satisfies the inequality 2 and satisfies the inequality 1.

therefore

it is a solution of the system

see the attached figure N 2


inequality 1

(1, 2)\\ x=1\\ y=2

2 < 5*(1) + 2

2 < 7 -----> is true

inequality 2

(1, 2)\\ x=1\\ y=2

2 \geq \frac{1}{2}*(1) + 1

2 \geq \frac{3}{2} -----> is true

case 5) (2,-1)

This point satisfies the inequality 1 but does not satisfy the inequality 2.

therefore

it not a solution of the system

see the attached figure N 2


inequality 1

(2, -1)\\ x=2\\ y=-1

-1 < 5*(2) + 2

-1 < 12 -----> is true

inequality 2

(2, -1)\\ x=2\\ y=-1

-1 \geq \frac{1}{2}*(2) + 1

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

case 6) (2, 2)

This point satisfies the inequality 1 and satisfies the inequality 2.

therefore

it is a solution of the system

see the attached figure N 2


inequality 1

(2, 2)\\ x=2\\ y=2

2 < 5*(2) + 2

2 < 12 -----> is true

inequality 2

(2, 2)\\ x=2\\ y=2

2 \geq \frac{1}{2}*(2) + 1

2 \geq 2 -----> is true

therefore

the answer is

case 4) (1, 2)\\ case 6) (2, 2)

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