Answer
$(1,5)$
Work Step by Step
We are given the system:
$\begin{cases}
y=4x+1\\
3x+2y=13
\end{cases}$
We will use the substitution method. Substitute the expression of $y$ in Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
y=4x+1\\
3x+2(4x+1)=13
\end{cases}$
$3x+2(4x+1)=13$
$3x+8x+2=13$
$11x+2=13$
$11x=11$
$x=1$
Substitute each the value of $x$ in the expression of $y$ to determine $y$:
$y=4x+1$
$x=1\Rightarrow y=4(1)+1=5$
The system's solution is:
$(1,5)$
