Question

a system of equations is given.
a: 2x + y = 8
b: -x - 4y = -12
if x is isolated in equation b, what expression is substituted into equation a for x?
4y + 12
4y - 12
-4y - 12
-4y + 12

Explanation:

Step1: Start with Equation B

We have Equation B: $-x - 4y = -12$. Our goal is to isolate $x$.

Step2: Add \(4y\) to both sides

Adding \(4y\) to both sides of the equation: $-x - 4y + 4y = -12 + 4y$. Simplifying the left side, we get $-x = -12 + 4y$.

Step3: Multiply both sides by \(-1\)

To solve for \(x\), multiply both sides of the equation $-x = -12 + 4y$ by \(-1\). This gives $x = 12 - 4y$, which can be rewritten as $x = -4y + 12$.

Answer:

\(-4y + 12\) (assuming the last option was meant to be \(-4y + 12\) as the text was cut off, and this is the correct expression for \(x\) when isolated from Equation B to substitute into Equation A)