Answer
$(2,2), (-2,-2)$
Work Step by Step
We are given the system:
$\begin{cases}
y-x=0\\
xy-4=0
\end{cases}$
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 $x$:
$\begin{cases}
y=x\\
x(x)-4=0
\end{cases}$
$x^2-4=0$
$(x-2)(x+2)=0$
$x-2=0\Rightarrow x_1=2$
$x+2=0\Rightarrow x_2=-2$
Substitute each of the values of $x$ in the expression of $y$ to determine $y$:
$y=x$
$x_1=2\Rightarrow y_1=2$
$x_2=-2\Rightarrow x_2=-2$
The system's solutions are:
$(2,2), (-2,-2)$
