Question

How do you solve `\sqrt { 7y + 5} = \sqrt { 6y + 9}`?

Answer 1

`y=4`

Explanation:

Given:

`sqrt(7y+5) = sqrt(6y+9)`

Square both sides of the equation to get:

`7y+5 = 6y+9`

Note that in general squaring both sides of an equation yields an equation that is required to hold, but may give extra solutions which are not solutions of the original equation.

Subtract `6y+5` from both sides to get:

`y = 4`

Note that this is a solution of the original equation, since:

`sqrt(7(color(blue)(4))+5) = sqrt(33) = sqrt(6(color(blue)(4))+9)`

(The same would not have been true had the original equation been: `sqrt(7y+5) = -sqrt(6y+9)`)