Question

step 1
$6x + 12y = 60$
$20x - 12y = 44$
step 2

step 3
$x = 4$
step 4
$2(4) + 4y = 20$
$8 + 4y = 20$
$4y = 12$
$y = 3$
step 5
the solution is $(4, 3)$.
what needs to be done in step 2?

• divide both sides of the equations in step 1 by the same number to eliminate one variable.
• multiply both sides of the equations in step 1 by the same number to eliminate one variable.
• add the equations in step 1 to eliminate one variable.
• subtract the equations in step 1 to eliminate one variable.

Explanation:

Step1: Analyze Step 1 equations

We have $6x + 12y = 60$ and $20x - 12y = 44$. Notice the coefficients of $y$ are $12$ and $-12$, which are additive inverses.

Step2: Identify elimination method

To eliminate $y$, we add the two equations, since $12y + (-12y) = 0$. This will let us solve for $x$, which matches the result $x=4$ in Step 3.

Answer:

Add the equations in step 1 to eliminate one variable.