Answer
\[\left\{ \left( 2,3 \right) \right\}\]
Work Step by Step
Find the value of y from the second equation as follows:
\[\begin{align}
& 2x-y=1 \\
& 2x-1=y \\
& y=2x-1 \\
\end{align}\]
Substitute the value of \[y=2x-1\]in the first equation and solve
\[\begin{align}
& x+4y=14 \\
& x+4\left( 2x-1 \right)=14 \\
& x+8x-4=14 \\
& 9x=14+4
\end{align}\]
Solve further as
\[\begin{align}
& 9x=18 \\
& x=\frac{18}{9} \\
& x=2 \\
\end{align}\]
Substitute the value of \[x=2\]in the second equation as follows:
\[\begin{align}
& 2x-y=1 \\
& 2\left( 2 \right)-y=1 \\
& 4-1=y \\
& y=3
\end{align}\]
Hence, the value of x is 2 and y is 3.
