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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.

Sagot :

Semsee45idn

Answer:

3x + 5y = 5

Multiply by 2 on both sides.

-2x - 8y = -6

Multiply by 3 on both sides.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]

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:

[tex]\implies 2(3x+5y)=2(5)[/tex]

[tex]\implies 6x+10y=10[/tex]

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

[tex]\implies 3(-2x - 8y) = 3(6)[/tex]

[tex]\implies -6x - 24y = 18[/tex]

Add them together to eliminate x:

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

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