Questions: Solve the following radical equation. Enter your answer as an integer. If there is no solution indicate "No Solution". sqrt(5y-1) = sqrt(2y+2) y = No Solution

Solution Steps

To eliminate the square roots, square both sides of the equation: \[ (\sqrt{5y - 1})^2 = (\sqrt{2y + 2})^2 \] This simplifies to: \[ 5y - 1 = 2y + 2 \]

Subtract \( 2y \) from both sides to isolate the variable: \[ 5y - 2y - 1 = 2 \] Simplify: \[ 3y - 1 = 2 \]

Add 1 to both sides: \[ 3y = 3 \] Divide both sides by 3: \[ y = 1 \]

Substitute \( y = 1 \) back into the original equation to ensure it is valid: \[ \sqrt{5(1) - 1} = \sqrt{2(1) + 2} \] Simplify: \[ \sqrt{4} = \sqrt{4} \] Since both sides are equal, \( y = 1 \) is the correct solution.

\[ y = 1 \]

Final Answer