Question

Which of the following points are solutions to the system of inequalities shown below

Answer 1

(4, 19)

(2, 11)

Explanation:

y ≥ 4x + 3

y > 1

To check which point satisfy the inequality we try all the points given.

(4, 11) ⇒ y = 11 and x = 4

11 ≥ 4×4 + 3 ⇒ 11 ≥ 19 Not true

y > 1 ⇒ 11 > 1 TRUE

(4, 19) ⇒ Y=19 and x = 4

19 ≥ 4×4 + 3 ⇒⇒ 19 ≥ 19 TRUE

y > 1 ⇒ 19 > 1 TRUE

(2, 11) ⇒ y=11 and x=2

11 ≥ 4×2 + 3 ⇒ 11 ≥ 11 TRUE

y > 1 ⇒ 11 > 1 TRUE

Answer 2

`(4,19)`

Explanation:

we have

`y\geq 4x+3` -----> inequality A

`x>1` -----> inequality B

we know that

If a ordered pair is a solution of the system of equations, then the ordered pair must satisfy both inequalities of the system of equations

verify each ordered pair

case A)
`(4,11)`

Verify inequality A

Substitute the value of x and the value of y in the inequality and then compare

`11\geq 4(4)+3`

`11\geq 19` -----> is not true

therefore

case A) is not a solution

case B)
`(1,-1)`

Verify inequality A

Substitute the value of x and the value of y in the inequality and then compare

`-1\geq 4(1)+3`

`-1\geq 7` -----> is not true

therefore

case B) is not a solution

case C)
`(1,11)`

Verify inequality A

Substitute the value of x and the value of y in the inequality and then compare

`11\geq 4(1)+3`

`11\geq 7` -----> is true

Verify inequality B

`1>1` -----> is not true

therefore

case C) is not a solution

case D)
`(4,19)`

Verify inequality A

Substitute the value of x and the value of y in the inequality and then compare

`19\geq 4(4)+3`

`19\geq 19` -----> is true

Verify inequality B

`4>1` -----> is true

therefore

case D) is a solution