Question

a variable needs to be eliminated to solve the system of equations below. choose the correct first step.

$4x - y = -21$

$-4x + 10y = 66$

answer attempt 1 out of 3

• subtract to eliminate x.
• add to eliminate x.
• subtract to eliminate y.
• add to eliminate y.

Explanation:

Step1: Analyze x coefficients

The coefficient of $x$ in the first equation is $4$, and in the second equation is $-4$.

Step2: Check elimination via addition

Adding the two equations: $(4x - y) + (-4x + 10y) = -21 + 66$. The $4x$ and $-4x$ terms cancel out, eliminating $x$.

Step3: Evaluate other options

Subtracting would not eliminate $x$ (it would give $8x -11y = -87$), and neither adding nor subtracting directly eliminates $y$ (coefficients of $y$ are $-1$ and $10$, which do not sum to 0 or are not equal).

Answer:

Add to eliminate x.