Question

which of the following values is the y-value of the solution to the given system of equations?
$-4y - 3 = x$
$2x - 22 = 6y$
a. $y = -2\frac{1}{2}$
b. $y = -2$
c. $y = -\frac{3}{4}$
d. $y = 5$

Explanation:

Step1: Substitute \( x \) into the second equation

We have \( x = -4y - 3 \) from the first equation. Substitute this into \( 2x - 22 = 6y \):
\( 2(-4y - 3) - 22 = 6y \)

Step2: Simplify the equation

Expand the left - hand side:
\( -8y - 6 - 22 = 6y \)
Combine like terms:
\( -8y - 28 = 6y \)

Step3: Solve for \( y \)

Add \( 8y \) to both sides:
\( -28 = 6y + 8y \)
\( -28 = 14y \)
Divide both sides by 14:
\( y=\frac{-28}{14}=-2 \)

Answer:

B. \( y = - 2 \)