Question

1. identify the ordered pairs that are solutions to the linear inequality ( 5x - y > 4 )?

(4,2)
(-3,1)
(5,-2)
(2,7)
(0,-1)
(8,4)

Explanation:

Step1: Rearrange the inequality

Rewrite $5x - y > 4$ to solve for $y$:
Subtract $5x$ from both sides: $-y > -5x + 4$
Multiply by $-1$ (reverse inequality): $y < 5x - 4$

Step2: Test (4, 2)

Substitute $x=4, y=2$:
$2 < 5(4) - 4$
$2 < 20 - 4$
$2 < 16$ ✔️

Step3: Test (5, -2)

Substitute $x=5, y=-2$:
$-2 < 5(5) - 4$
$-2 < 25 - 4$
$-2 < 21$ ✔️

Step4: Test (0, -1)

Substitute $x=0, y=-1$:
$-1 < 5(0) - 4$
$-1 < -4$ ❌

Step5: Test (-3, 1)

Substitute $x=-3, y=1$:
$1 < 5(-3) - 4$
$1 < -15 - 4$
$1 < -19$ ❌

Step6: Test (2, 7)

Substitute $x=2, y=7$:
$7 < 5(2) - 4$
$7 < 10 - 4$
$7 < 6$ ❌

Step7: Test (8, 4)

Substitute $x=8, y=4$:
$4 < 5(8) - 4$
$4 < 40 - 4$
$4 < 36$ ✔️

Answer:

(4, 2), (5, -2), (8, 4)