Question

Solve: ( x + y = x² - y² = 23 ), find ( y ).

• A. 11
• B. 12
• C. 24
• D. 36
• E.

Hint:

For quadratic equations, factor or expand the terms and substitute known values to solve step-by-step.

Answer 1

The Correct Option is A

Step 1: From the equation \( x + y = 23 \), we have: \[ x + y = 23 \quad \Rightarrow \quad x = 23 - y. \] Step 2: Substituting \( x = 23 - y \) into \( x^2 - y^2 = 23 \): \[ (23 - y)^2 - y^2 = 23. \] Step 3: Expanding the equation: \[ (529 - 46y + y^2) - y^2 = 23 \quad \Rightarrow \quad 529 - 46y = 23. \] Step 4: Solving for \( y \): \[ 529 - 23 = 46y \quad \Rightarrow \quad 506 = 46y \quad \Rightarrow \quad y = \frac{506}{46} = 11. \]