We have to solve this system of linear equations.
As we have the same coefficient for y, the most effective method to solve this is by elimination: we substract the first equation from the second one and then solve for x, as y is no longer part of this new equation.
We then substract the equations:
[tex]\begin{gathered} (3x+7y)-(5x+7y)=11-9 \\ 3x-5x+7y-7y=2 \\ -2x+0y=2 \\ -2x=2 \end{gathered}[/tex]
Then, we can solve for x:
[tex]\begin{gathered} -2x=2 \\ x=\frac{2}{-2} \\ x=-1 \end{gathered}[/tex]
Then, we can pick any of the two equations and, with the value of x = -1, we can solve for y as:
[tex]\begin{gathered} 5x+7y=9 \\ 5(-1)+7y=9 \\ -5+7y=9 \\ 7y=9+5 \\ 7y=14 \\ y=\frac{14}{7} \\ y=2 \end{gathered}[/tex]
Answer: x = -1 and y = 2.
