Answer
$(2,3)$
Work Step by Step
We are given the system:
$\begin{cases}
2x-y=1\\
x+4y=14
\end{cases}$
We will use the addition method. Multiply Equation 1 by 4 and add it to Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
4(2x-y)=4(1)\\
x+4y=14
\end{cases}$
$\begin{cases}
8x-4y=4\\
x+4y=14
\end{cases}$
$8x-4y+x+4y=4+14$
$9x=18$
$x=2$
Substitute the value of $x$ in Equation 1 to determine $y$:
$2x-y=1$
$2(2)-y=1$
$4-y=1$
$y=3$
The system's solution is:
$(2,3)$
