Answer
$(1,-3)$
Work Step by Step
We are given the system:
$\begin{cases}
x=y+4\\
3x+7y=-18
\end{cases}$
We will use the substitution method. Equation 1 is solved for $x$. We substitute the expression of $x$ in Equation 2 to eliminate $x$ and determine $y$:
$\begin{cases}
x=y+4\\
3(y+4)+7y=-18
\end{cases}$
$3(y+4)+7y=-18$
$3y+12+7y=-18$
$10y+12=-18$
$10y=-30$
$y=-3$
Substitute the value of $y$ in the expression of $x$ to determine $x$:
$x=y+4$
$x=-3+4$
$x=1$
The system's solution is:
$(1,-3)$
