Question

14
$y < -5x - 19$
$y > -3x - 12$
for which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given system of inequalities?
a

$x$	$y$
$-6$	$9$
$-8$	$-4$

b

$x$	$y$
$-6$	$10$
$-8$	$19$

c

$x$	$y$
$-6$	$9$
$-8$	$19$

d

$x$	$y$
$-6$	$16$
$-8$	$-4$

Explanation:

Step1: Check Option A (x=-5,y=6)

First inequality: $6 < -5(-5)-19 = 25-19=6$? No (6 is not <6).

Step2: Check Option B (x=-5,y=4)

Second inequality: $4 > -3(-5)-12=15-12=3$? Yes. First inequality: $4 < 6$? Yes. Next (x=-6,y=10): First inequality $10 < -5(-6)-19=30-19=11$? Yes. Second inequality $10 > -3(-6)-12=18-12=6$? Yes. Next (x=-8,y=19): First inequality $19 < -5(-8)-19=40-19=21$? Yes. Second inequality $19 > -3(-8)-12=24-12=12$? Yes. Wait, correction: Recheck Option B x=-8,y=19: 19 <21 yes, 19>12 yes. Wait Option C x=-5,y=2: 2<6 yes, 2>3? No! Wait mistake: Recheck second inequality for Option B x=-5,y=4: 4>3 yes. Option C x=-5,y=2: 2>3? No. Option D x=-5,y=1:1>3? No. Option A x=-5,y=6:6<6 no. So correct is Option B? Wait no: Wait Option B x=-8,y=19: 19 < -5(-8)-19=40-19=21 yes; 19> -3(-8)-12=24-12=12 yes. Option C x=-5,y=2: 2>3? No. So correct answer is B? Wait original problem Option C: Let me recheck. Oh no, I messed up Option C: Option C x=-5,y=2: 2> -3*(-5)-12=15-12=3? No. So Option B is correct? Wait the user's options: Let me recheck the problem. The user's Option B: x=-5,y=4; x=-6,y=10; x=-8,y=19. All satisfy both inequalities. So answer is B.

Wait final correction:

Step1: Verify Option A

x=-5,y=6: $6 < 6$? No. Reject.

Step2: Verify Option B

x=-5,y=4: $4 <6$ and $4>3$? Yes.
x=-6,y=10: $10 <11$ and $10>6$? Yes.
x=-8,y=19: $19 <21$ and $19>12$? Yes.

Step3: Verify Option C

x=-5,y=2: $2>3$? No. Reject.

Step4: Verify Option D

x=-5,y=1: $1>3$? No. Reject.

Thus, correct answer is B.

Answer:

C. Option C