Question

what would be the first step for solving the system below using elimination to eliminate the ys? \

$$\begin{cases} 2x - y = 8 \\\\ 3x + 3y = 22 \\end{cases}$$

\
a add the 2 equations \
b multiply 1st equation by 3 \
c multiply 2nd equation by -1 \
d multiply 1st equation by 3

Explanation:

Step1: Analyze elimination goal

We aim to eliminate $y$. The first equation has $-y$, the second has $+3y$.

Step2: Match coefficient of $y$

To make the coefficients of $y$ opposites or equal, multiply the first equation by 3:
$3\times(2x - y) = 3\times8$ → $6x - 3y = 24$. Now $y$ terms are $-3y$ and $+3y$, which can be eliminated by adding equations.

Step3: Evaluate other options

• Adding equations directly does not eliminate $y$.
• Multiplying first equation by -3 gives $-6x+3y=-24$, which doesn't set up immediate elimination for $y$ as cleanly as multiplying by 3.
• Multiplying second equation by -1 gives $-3x-3y=-22$, which doesn't align with the first equation's $y$ term for elimination.

Answer:

B. Multiply 1st equation by 3