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Sagot :
The given system of equations is
[tex]\begin{gathered} 6x+5y=-2\rightarrow(1) \\ -7x-9y=-23\rightarrow(2) \end{gathered}[/tex]Multiply equation (1) by 7 and equation (2) by 6 to make the coefficients of x equal in values and different in signs to eliminate x
[tex]\begin{gathered} 7(6x)+7(5y)=7(-2) \\ 42x+35y=-14\rightarrow(3) \end{gathered}[/tex][tex]\begin{gathered} 6(-7x)-6(9y)=6(-23) \\ -42x-54y=-138\rightarrow(4) \end{gathered}[/tex]Add equations (3) and (4) to eliminate x
[tex]\begin{gathered} (42x-42x)+(35y-54y)=(-14-138) \\ -19y=-152 \end{gathered}[/tex]Divide both sides by -19 to find y
[tex]\begin{gathered} \frac{-19y}{-19}=\frac{-152}{-19} \\ y=8 \end{gathered}[/tex]Substitute y by 8 in equation (1) to find x
[tex]\begin{gathered} 6x+5(8)=-2 \\ 6x+40=-2 \end{gathered}[/tex]Subtract 40 from both sides
[tex]\begin{gathered} 6x+40-40=-2-40 \\ 6x=-42 \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{6x}{6}=\frac{-42}{6} \\ x=-7 \end{gathered}[/tex]The solution of the system is (-7, 8)
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