Question

1. what should be done to these equations in order to solve a system of equations by elimination?\

$$\begin{cases}-3x + 2y = 16\\\\2x + 5y = 21\\end{cases}$$

\bigcirc multiply the first equation by 3.\bigcirc nothing needs to be done, since they both equal have 2s and 3s for coefficients.\bigcirc multiply the first equation by 3 and the second equations by 2.\bigcirc multiply the first equation by 2 and the second equation by 3.

Explanation:

Step1: Recall elimination method goal

The elimination method requires creating opposite coefficients for one variable so they cancel when equations are added.

Step2: Analyze x-coefficients

First equation x-coefficient: $-3$; second: $2$. We need to make their absolute values equal.

Step3: Find common multiple

The least common multiple of 3 and 2 is 6. Multiply first equation by 2: $2(-3x + 2y) = 2(16) \implies -6x + 4y = 32$. Multiply second equation by 3: $3(2x + 5y) = 3(21) \implies 6x + 15y = 63$. Now x-coefficients are $-6$ and $6$, which are opposites.

Step4: Evaluate options

Only the last option matches this required operation.

Answer:

D. Multiply the first equation by 2 and the second equation by 3.