We have to solve the system:
[tex]\begin{gathered} -\frac{5}{7}-\frac{11}{7}x=-y \\ 2y=7+5x \end{gathered}[/tex]To solve this system by elimination we have to add or substract a linear combination of the second equation from the first equation in order to eliminate one of the variables.
In this case we can multiply the first equation by 2 and add it to the second equation:
[tex]\begin{gathered} -y\cdot2=(-\frac{5}{7}-\frac{11}{7}x)\cdot2 \\ -2y=-\frac{10}{7}-\frac{22}{7}x \end{gathered}[/tex][tex]\begin{gathered} -2y+2y=(-\frac{10}{7}-\frac{22}{7}x)+(7+5x) \\ 0=-\frac{10}{7}-\frac{22}{7}x+7+5x \\ \frac{22}{7}x-5x=7-\frac{10}{7} \\ \frac{22x-5\cdot7x}{7}=\frac{7\cdot7-10}{7} \\ 22x-35x=49-10 \\ -13x=39 \\ x=\frac{39}{-13} \\ x=-3 \end{gathered}[/tex]Now we can use any of the two equations to find y:
[tex]\begin{gathered} -y=-\frac{5}{7}-\frac{11}{7}x \\ y=\frac{5}{7}+\frac{11}{7}(-3) \\ y=\frac{5}{7}-\frac{33}{7} \\ y=-\frac{28}{7} \\ y=-4 \end{gathered}[/tex]Answer: x=-3 and y=-4
