Answer
\[x=-6,\ y=-2\]
Work Step by Step
Multiply \[7\]on both sides to the equation \[3x+y=-20\]to get: \[21x+7y=-140\].
Add the second given equation to the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 2x-7y=2 \\
& 21x+7y=-140
\end{align}}\]
\[\begin{align}
& 23x\ \ \ \ \ \ \ \ =-138 \\
& x=-6
\end{align}\]
Put \[x=-6\]in\[2x-7y=2\], to get:
\[\begin{align}
& 2\left( -6 \right)-7y=2 \\
& -12-7y=2 \\
& -7y=14 \\
& y=-2
\end{align}\]
Put\[x=-6\]and \[y=-2\]in any of the given equations to check the solution:
\[\begin{align}
& 3\left( -6 \right)+\left( -2 \right)=-20 \\
& -18-2=-20 \\
& -20=-20
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Now check with 2x -7y = 2:
2(-6) -7(-2) = 2
-12+14 = 2
2 = 2
Hence, x = -6. y = -2 is the solution of this system of equations.
