Answer
$(0,-3), (2,1)$
Work Step by Step
We are given the system:
$\begin{cases}
2x-y=3\\
(x-1)^2+(y+1)^2=5
\end{cases}$
We will use the substitution method. Solve Equation 1 for $y$ and substitute the expression of $y$ in Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
y=2x-3\\
(x-1)^2+(2x-3+1)^2=5
\end{cases}$
$(x-1)^2+(2x-2)^2=5$
$x^2-2x+1+4x^2-8x+4=5$
$5x^2-10x+5-5=0$
$5x^2-10x=0$
$5x(x-2)=0$
$x=0\Rightarrow x_1=0$
$x-2=0\Rightarrow x_2=2$
Substitute each of the values of $x$ in the expression of $y$ to determine $y$:
$y=2x-3$
$x_1=0\Rightarrow y_1=2(0)-3=-3$
$x_2=2\Rightarrow y_2=2(2)-3=1$
The system's solutions are:
$(0,-3), (2,1)$
