Answer
The system has an infinite number of solutions.
Solution set = $\{(x,y)\ |\ y=x\}$
Work Step by Step
Graph each line
(plot two points per line, such as the intercepts)
$x-y=0:\quad \left[\begin{array}{lll}
x=0 & ... & x=1\\
0-y=0 & & 1-y=0 \\
y=0 & & y=1\\
(0,0) & & (1,1)
\end{array}\right]$
$y=x:\quad \left[\begin{array}{lll}
x=0 & ... & x=1\\
y=0 & & y=1\\
& & \\
(0,0) & & (1,1)
\end{array}\right]$
The lines coincide.
The system has an infinite number of solutions.
Solution set = $\{(x,y)\ |\ y=x\}$
