Question

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$$\begin{cases} 8x + 5y = -7 \\\\ -7x + 6y = -4 \\end{cases}$$

choose 1 answer:

\\(\boldsymbol{\text{a}}\\) multiply the top equation by 6, multiply the bottom equation by \\(-5\\), then add the equations.

\\(\boldsymbol{\text{b}}\\) multiply the top equation by 7, then add the equations.

\\(\boldsymbol{\text{c}}\\) multiply the bottom equation by 8, then add the equations.

Explanation:

Step1: Analyze elimination goal

We aim to eliminate one variable. Let's check each option for eliminating $y$ or $x$.

Step2: Evaluate Option A

Multiply top eq by 6: $6*(8x+5y)=6*(-7) \implies 48x + 30y = -42$
Multiply bottom eq by $-5$: $-5*(-7x+6y)=-5*(-4) \implies 35x - 30y = 20$
Add equations: $(48x+35x)+(30y-30y)=-42+20 \implies 83x=-22$. This eliminates $y$, valid.

Step3: Evaluate Option B

Multiply top eq by 7: $7*(8x+5y)=7*(-7) \implies 56x + 35y = -49$
Add to bottom eq: $(56x-7x)+(35y+6y)=-49-4 \implies 49x+41y=-53$. No variable eliminated, invalid.

Step4: Evaluate Option C

Multiply bottom eq by 8: $8*(-7x+6y)=8*(-4) \implies -56x + 48y = -32$
Add to top eq: $(8x-56x)+(5y+48y)=-7-32 \implies -48x+53y=-39$. No variable eliminated, invalid.

Answer:

A. Multiply the top equation by 6, multiply the bottom equation by $-5$, then add the equations.