Question

2a. which variable is eliminated (canceled out) if one of the two equations is multiplied by -1 and then they are combined (added together)?
\

$$\begin{cases}10x + 3y = -42\\\\10x - 7y = -2\\end{cases}$$

\bigcirc x
\bigcirc y

Explanation:

Step1: Multiply first equation by -1

$-1\times(10x + 3y) = -1\times(-42)$
$\implies -10x - 3y = 42$

Step2: Add to second equation

$(-10x - 3y) + (10x - 7y) = 42 + (-2)$
$\implies (-10x+10x) + (-3y-7y) = 40$
$\implies 0x -10y = 40$

Step3: Identify eliminated variable

The $x$-terms sum to 0, so $x$ is eliminated.

Answer:

x