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8x+5y=-13
3x+4y=10
what is the x and y using elimination?

1 Answer

3 votes


\begin{cases}8x+5y=-13\\3x+4y=10\end{cases}

Multiply both equations by appropriate constants to get the coefficients of either
x or
y in both equations to be the same. One choice would be to multiply the first equation by 3 and the second by 8:


\begin{cases}24x+15y=-39\\24x+32y=80\end{cases}

Then subtract either equation from the other to eliminate
x. I'll take the first from the second:


(24x+32y)-(24x+15y)=80-(-39)\implies17y=119\implies y=7

Then solve for
x in either equation. From the second one, we find


3x+4(7)=10\implies3x=10-28=-18\implies x=-6

So the solution to this system is the coordinate pair (-6, 7).

User Desmon
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