Question

The ordered pair(5,-3) is a solution to which of the following inequalities? a. y≥−2x+8 b. −2y<3x−9 c. y−2x>5 d. 4y+2x≤−1

Answer 1

Answer:

Option d. $4y+2x\leq -1$

Step-by-step explanation:

we know that

If a ordered pair is a solution of an inequality, then the ordered pair must be satisfy the inequality

Verify each case

case a) $y\geq2x+8$

we have

$x=5, y=-3$

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

$-3\geq2(5)+8$

$-3\geq18$ -----> is not true

therefore

the ordered pair is not a solution

case b) $-2y$

we have

$x=5, y=-3$

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

$-2(-3)$

$6$ -----> is not true

therefore

the ordered pair is not a solution

case c) $y-2x>5$

we have

$x=5, y=-3$

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

$-3-2(5)>5$

$-13>5$ -----> is not true

therefore

the ordered pair is not a solution

case d) $4y+2x\leq -1$

we have

$x=5, y=-3$

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

$4(-3)+2(5)\leq -1$

$-2\leq -1$ -----> is  true

therefore

the ordered pair is a solution