Answer
\[x=2,\ y=-1\]
Work Step by Step
Multiply \[5\]on both sides to the equation \[3x-7y=13\]to get: \[15x-35y=65\].
Multiply \[7\]on both sides to the equation \[6x+5y=7\]to get: \[42x+35y=49\].
Add the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 15x-35y=65 \\
& 42x-35y=49
\end{align}}\]
\[\begin{align}
& 57x\ \ \ \ \ \ \ \ \ \ =114 \\
& x=2
\end{align}\]
Put \[x=2\]in\[3x-7y=13\], to get:
\[\begin{align}
& 3\left( 2 \right)-7y=13 \\
& 6-7y=13 \\
& -7y=7 \\
& y=-1
\end{align}\]
Put\[x=2\]and \[y=-1\]in any of the given equations to check the solution:
\[\begin{align}
& 6\left( 2 \right)+5\left( -1 \right)=7 \\
& 12-5=7 \\
& 7=7
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Now, check with other equation 3x – 7y = 13 too.
3(2) -7(-1) = 13
6 +7 = 13
13 = 13
LHS = RHS.So, this is the solution to this system of equations.
