Answer
The system of linear equations has only one solution and the solution set is\[\left\{ \left( 3,-2 \right) \right\}\].
Work Step by Step
Multiply \[5\]on both sides to the equation \[3x-y=11\]to get: \[15x-5y=55\].
Add the second given equation to the above-obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 2x+5y=-4 \\
& 15x-5y=55
\end{align}}\]
\[\begin{align}
& 17x\ \ \ \ \ \ \ =51 \\
& x=3
\end{align}\]
Put \[x=3\]in\[3x-y=11\], to get:
\[\begin{align}
& 3\left( 3 \right)-y=11 \\
& 9-y=11 \\
& -y=2 \\
& y=-2
\end{align}\]
Put\[x=3\]and \[y=-2\]in any of the provided equations to check the solution,
\[\begin{align}
& 2\left( 3 \right)+5\left( -2 \right)=-4 \\
& 6-10=-4 \\
& -4=-4
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Hence the set \[\left\{ \left( 3,-2 \right) \right\}\]is the solution set of the provided system of linear equations.
