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Sagot :
To solve the system of equations:
[tex]\begin{gathered} -5x-7y=23 \\ 3x+4y=-12 \end{gathered}[/tex]We can do by adding equations. To do that, we need to make the coefficient of one of the variables the same but with different signs.
We can do that with x by multiplying the first equations by 3 and the second by 5:
[tex]\begin{gathered} -5x+7y=23\leftrightarrow-15x-21y=69 \\ 3x+4y=-12\leftrightarrow15x+20y=-60 \end{gathered}[/tex]Now, we add them:
[tex]\begin{gathered} -15x-21y=69 \\ 15x+20y=-60 \\ 0x-1y=9 \\ -y=9 \\ y=-9 \end{gathered}[/tex]Now, we can substitute y into either equation to find out x:
[tex]\begin{gathered} -5x-7y=23 \\ -5x-7\cdot(-9)=23 \\ -5x+63=23 \\ -5x=23-63 \\ -5x=-40 \\ x=\frac{-40}{-5} \\ x=8 \end{gathered}[/tex]So, the solution is:
[tex]\begin{gathered} x=8 \\ y=-9 \end{gathered}[/tex]
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