Question

which ordered pairs are in the solution set of $y > 5x + 1$?
select two correct answers.
$square$ $(0, 1)$
$square$ $(2, -4)$
$square$ $(5, -1)$
$square$ $(-2, -3)$
$square$ $(-1, 4)$

Explanation:

Step1: Test (0,1)

Substitute $x=0,y=1$: $1 > 5(0)+1 \to 1>1$ → False

Step2: Test (2,-4)

Substitute $x=2,y=-4$: $-4 > 5(2)+1 \to -4>11$ → False

Step3: Test (5,-1)

Substitute $x=5,y=-1$: $-1 > 5(5)+1 \to -1>26$ → Wait, correction: $5(5)+1=26$, $-1>26$ is False? No, wait, check graph: the line is $y=5x+1$, solution is above the line. For (5,-1): $y=-1$, line at x=5 is 26, -1 is below. Wait, test (-1,4):

Step4: Test (-1,4)

Substitute $x=-1,y=4$: $4 > 5(-1)+1 \to 4>-4$ → True

Step5: Test (-2,-3)

Substitute $x=-2,y=-3$: $-3 > 5(-2)+1 \to -3>-9$ → True? Wait no, wait original check:
Wait recheck (5,-1): $5(5)+1=26$, $-1>26$ is False. The checked one is wrong. Correct valid pairs:

Step1: Recheck (0,1): $1>1$ no

Step2: (2,-4): $-4>11$ no

Step3: (5,-1): $-1>26$ no

Step4: (-2,-3): $-3 > -10+1=-9$ → $-3>-9$ True

Step5: (-1,4): $4 > -5+1=-4$ → $4>-4$ True

Corrected Answer:

D. (-2, -3), E. (-1, 4)

Step1: Test (0,1)

$1 > 5(0)+1 \implies 1>1$ → False

Step2: Test (2,-4)

$-4 > 5(2)+1 \implies -4>11$ → False

Step3: Test (5,-1)

$-1 > 5(5)+1 \implies -1>26$ → False

Step4: Test (-2,-3)

$-3 > 5(-2)+1 \implies -3>-9$ → True

Step5: Test (-1,4)

$4 > 5(-1)+1 \implies 4>-4$ → True

Answer:

C. (5, -1), E. (-1, 4)