Question

which of these strategies would eliminate a variable in the system of equations?\

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

choose 1 answer:\
a multiply the top equation by 6, multiply the bottom equation by -5, then add the equations.\
b multiply the top equation by 7, then add the equations.\
c multiply the bottom equation by 8, then add the equations.

Explanation:

Step1: Test Option A

Multiply top equation by 6: $6(8x + 5y) = 6(-7) \implies 48x + 30y = -42$
Multiply bottom equation by $-5$: $-5(-7x + 6y) = -5(-4) \implies 35x - 30y = 20$
Add equations: $(48x+30y)+(35x-30y)=-42+20 \implies 83x = -22$
The $y$-variable is eliminated.

Step2: Test Option B

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

Step3: Test Option C

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

Answer:

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