Solve the equation. sqrt(25y^2+40y+16)=5y+4

Question

Solve the equation.
`sqrt(25y^2+40y+16)=5y+4`

Answer 1

`√(25y^2+40y+16)=5y+4\implies \stackrel{\textit{squaring both sides}}{25y^2+40y+16=(5y+4)^2} \\\\\\ 25y^2+40y+16=25y^2+40y+16\hspace{5em}\textit{infinitely many solutions}`

the equation on the left is really the equation on the right in disguise.

for a system of equations, that usually means that one equation is the same as the other, so the graph will be the graph of the second one pancaked over the first one, where they touch each other all the way, and since both lines go to infinity, then they have infintely many solutions.