The 2 equations given,
[tex]\begin{gathered} 2x+3y=6 \\ -7x-5y=1 \end{gathered}[/tex]
Let's multiply the first equation by "7" and the second equation by "2". We have,
[tex]\begin{gathered} 7\times\lbrack2x+3y=6\rbrack \\ 2\times\lbrack-7x-5y=1\rbrack \\ ------------- \\ 14x+21y=42 \\ -14x-10y=2 \\ \end{gathered}[/tex]
Now we add both equations and solve for "y":
[tex]\begin{gathered} 14x+21y=42 \\ -14x-10y=2 \\ ----------- \\ 11y=44 \\ y=\frac{44}{11} \\ y=4 \end{gathered}[/tex]
Now we substitute this value of y into the original first equation and solve for x:
[tex]\begin{gathered} 2x+3y=6 \\ 2x+3(4)=6 \\ 2x+12=6 \\ 2x=6-12 \\ 2x=-6 \\ x=-\frac{6}{2} \\ x=-3 \end{gathered}[/tex]
So, the solution set is,
[tex](x,y)=(-3,4)[/tex]
