Question

card 2
for which equation is (-4, 2) a solution?
select all that apply.
a. $y = -x - 2$
b. $4y = 2x + 16$
c. $y = \frac{1}{2}x$

Explanation:

Step1: Check Option A

Substitute \( x = -4 \), \( y = 2 \) into \( y = -x - 2 \).
Right - hand side: \( -(-4)-2=4 - 2 = 2 \), which is equal to \( y = 2 \). So \((-4,2)\) is a solution for option A.

Step2: Check Option B

Substitute \( x=-4 \), \( y = 2 \) into \( 4y=2x + 16 \).
Left - hand side: \( 4\times2=8 \).
Right - hand side: \( 2\times(-4)+16=-8 + 16 = 8 \).
Since left - hand side = right - hand side, \((-4,2)\) is a solution for option B.

Step3: Check Option C

Substitute \( x = -4 \), \( y = 2 \) into \( y=\frac{1}{2}x \).
Right - hand side: \(\frac{1}{2}\times(-4)=-2\), which is not equal to \( y = 2 \). So \((-4,2)\) is not a solution for option C.

Answer:

A. \( y=-x - 2 \), B. \( 4y = 2x+16 \)