Answer
$y=4$ and $y=1$.
Work Step by Step
$y=\sqrt {5y-4}$
Squaring the above equation, we get
$y^{2}=5y-4$
$\implies y^{2}-5y+4=0$
Factoring, we have
$ (y-4)(y-1)=0$
Using the Zero-product property, we obtain
$y-4=0$ or $y-1=0$
Solving for $y$, we get
$y=4$ or $y=1$.
We check the results:
$\sqrt{5(4)-4}=\sqrt{16}=4\checkmark$
$\sqrt{5(1)-4}=\sqrt{1}=1\checkmark$
Both $y=4$ and $y=1$ satisfy the original equation. Therefore, the solutions are $y=4$ and $y=1$.
