Answer
$(1,0), (4,3)$
Work Step by Step
We are given the system:
$\begin{cases}
x-y=1\\
5y=x^2-1
\end{cases}$
We will use the substitution method. Solve Equation 1 for $x$ and substitute the expression of $x$ in Equation 2 to eliminate $x$ and determine $y$:
$\begin{cases}
x=y+1\\
5y=(y+1)^2-1
\end{cases}$
$5y=(y+1)^2-1$
$5y=y^2+2y+1-1$
$5y=y^2+2y$
$y^2-3y=0$
$y(y-3)=0$
$y=0\Rightarrow y_1=0$
$y-3=0\Rightarrow y_2=3$
Substitute each of the values of $y$ in the expression of $x$ to determine $x$:
$x=y+1$
$y_1=0\Rightarrow x_1=0+1=1$
$y_2=3\Rightarrow x_2=3+1=4$
The system's solutions are:
$(1,0), (4,3)$
