Question

question 3 of 40
which of these steps will eliminate a variable in this system?
$6x - 3y = 8$
$2x + 6y = 16$

a. multiply the second equation by 3. then subtract the second equation from the first.
b. multiply the second equation by 2. then add the equations.
c. multiply the second equation by 3. then add the equations.
d. multiply the first equation by 2. then subtract the second equation from the first.

Explanation:

Step1: Analyze Option A

Multiply second equation by 3: $6x + 18y = 48$. Subtract from first: $(6x-3y)-(6x+18y)=8-48 → -21y=-40$ (y remains, no elimination).

Step2: Analyze Option B

Multiply second equation by 2: $4x + 12y = 32$. Add to first: $(6x-3y)+(4x+12y)=8+32 → 10x+9y=40$ (both variables remain).

Step3: Analyze Option C

Multiply second equation by 3: $6x + 18y = 48$. Add to first: $(6x-3y)+(6x+18y)=8+48 → 12x+15y=56$ (both variables remain).

Step4: Analyze Option D

Multiply first equation by 2: $12x - 6y = 16$. Subtract second equation: $(12x-6y)-(2x+6y)=16-16 → 10x=0$ (y eliminated).

Answer:

D. Multiply the first equation by 2. Then subtract the second equation from the first.