Question

At what points will the line
y = x
intersect the unit circle
x2 + y2 = 1?

Answer 1

since \(y=x\) you can solve
\[x^2+x^2=1\] for \(x\)

Answer 2

takes only a couple of steps, but be careful
\[2x^2=1\\x^2=\frac{1}{2}\\x=\pm\frac{1}{\sqrt2}\]