Question

3x + 5y = 5

-2x-8y = 6
How can you eliminate the x-terms in this system?
3x + 5y = 5
Multiply by ? on both sides.
-2x8y=-6
Multiply by ?
on both sides.

Answer 1

3x + 5y = 5

Multiply by 2 on both sides.

-2x - 8y = -6

Multiply by 3 on both sides.

Explanation:

Given system of equations:

`\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}`

To eliminate the x-terms in the given system of equations:

• Multiply 3x + 5y = 5 by 2 on both sides.
• Multiply -2x - 8y = 6 by 3 on both sides>

3x + 5y = 5 → Multiply by 2 on both sides:

`\implies 2(3x+5y)=2(5)`

`\implies 6x+10y=10`

-2x - 8y = 6 → Multiply by 3 on both sides:

`\implies 3(-2x - 8y) = 3(6)`

`\implies -6x - 24y = 18`

Add them together to eliminate x:

`\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}`