Question

Solve for \( y \): \( y^2 - 9 = 0 \).

• A. \( y = 3 \)
• B. \( y = -3 \)
• C. \( y = 0 \)
• D. No solution

Hint:

When solving quadratic equations that can be factored, set each factor equal to zero to find the possible solutions.

Answer 1

The Correct Option is A

We are asked to solve the quadratic equation: \[ y^2 - 9 = 0. \] This equation can be factored as a difference of squares. Recall the formula for factoring a difference of squares: \[ a^2 - b^2 = (a - b)(a + b). \] Applying this to the equation \( y^2 - 9 \), we recognize that it is in the form of \( a^2 - b^2 \) where \( a = y \) and \( b = 3 \). Therefore, we can factor the equation as: \[ (y - 3)(y + 3) = 0. \] Next, to solve for \( y \), we set each factor equal to zero: \[ y - 3 = 0
\text{or}
y + 3 = 0. \] Solving each equation: - From \( y - 3 = 0 \), we add 3 to both sides to get: \[ y = 3. \] - From \( y + 3 = 0 \), we subtract 3 from both sides to get: \[ y = -3. \] Thus, the two possible solutions are: \[ y = 3
\text{or}
y = -3. \] Therefore, the solution to the equation is \( y = 3 \) or \( y = -3 \).