Question

Which point would be a solution to the system of linear inequalities ?

Answer 1

(12,-6)

Explanation:

we have

`y\leq (4)/(3)x+5` ----> inequality A

`y\geq -(5)/(2)x+5` ---> 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 point

Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B

case 1) (0,-1)

Inequality A

`-1\leq (4)/(3)(0)+5`

`-1\leq5` ----> is true

Inequality B

`-1\geq -(5)/(2)(0)+5`

`-1\geq 5` ----> is not true

therefore

The ordered pair is not a solution of the system

case 2) (0,3)

Inequality A

`3\leq (4)/(3)(0)+5`

`3\leq5` ----> is true

Inequality B

`3\geq -(5)/(2)(0)+5`

`3\geq 5` ----> is not true

therefore

The ordered pair is not a solution of the system

case 3) (-6,-6)

Inequality A

`-6\leq (4)/(3)(-6)+5`

`-6\leq-3` ----> is true

Inequality B

`-6\geq -(5)/(2)(-6)+5`

`-6\geq 20`----> is not true

therefore

The ordered pair is not a solution of the system

case 4) (12,-6)

Inequality A

`-6\leq (4)/(3)(12)+5`

`-6\leq21` ----> is true

Inequality B

`-6\geq -(5)/(2)(12)+5`

`-6\geq -25` ----> is true

therefore

The ordered pair is a solution of the system (makes true both inequalities)