Question

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

Answer 1

Answer:

$(4,19)$

Step-by-step 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

Answer 2

Answer:

(4, 19)

(2, 11)

Step-by-step 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