Answer
\[\left\{ \left( 1,5 \right) \right\}\]
Work Step by Step
Substitute the value of \[y=4x+1\]in the second equation and solve
\[\begin{align}
& 3x+2y=13 \\
& 3x+2\left( 4x+1 \right)=13 \\
& 3x+8x+2=13 \\
& 11x=13-2
\end{align}\]
Solve further as
\[\begin{align}
& 11x=11 \\
& x=\frac{11}{11} \\
& x=1 \\
\end{align}\]
Substitute the value of \[x=1\]in the first equation as follows:
\[\begin{align}
& y=4x+1 \\
& =4\left( 1 \right)+1 \\
& =4+1 \\
& =5
\end{align}\]
Hence, the value of x is 1 and y is 5.
