Question

Which of the following would be a possible solution to the system of inequalities given below?

Answer 1

(0,5)

Explanation:

we have

`2x+3y > 12` ----> inequality A

`x-y\leq 1` ----> 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 of the system (makes true both inequalities)

Verify each ordered pair

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

case 1) (0,5)

For x=0,y=5

Inequality A

`2(0)+3(5) > 12`

`15 > 12` ----> is true

so

The ordered pair satisfy inequality A

Inequality B

`0-5\leq 1`

`-5\leq 1` ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair would be a solution of the system

case 2) (5,2)

For x=5,y=2

Inequality A

`2(5)+3(2) > 12`

`16 > 12` ----> is true

so

The ordered pair satisfy inequality A

Inequality B

`5-2\leq 1`

`3\leq 1` ---> is not true

so

The ordered pair not satisfy inequality B

therefore

The ordered pair is not a solution of the system

case 3) (0,4)

For x=0,y=4

Inequality A

`2(0)+3(4) > 12`

`12 > 12` ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system

case 4) (6,0)

For x=6,y=0

Inequality A

`2(6)+3(0) > 12`

`12 > 12` ----> is not true

so

The ordered pair not satisfy inequality A

therefore

The ordered pair is not a solution of the system