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