Algebra 2

You can set the equations equal to each other so that

$x\quad =\quad { x }^{ 2 }$

since they are both equal to y. Do not divide both sides by x. Instead, subtract x from both sides and factor to get

$0\quad =\quad { x }(x-1)$ .

There are two possible solutions: 0 and 1. Thus, the two graphs intersect twice. If you divided both sides by x in the previous steps, you would have lost the 0 since you would have gotten

$\frac { x }{ x } \quad =\quad \frac { { x }^{ 2 } }{ x }$

and then

$1=x$