Question

Solve: \(x+y=x^2-y^2=23\) find \(y\)

• A. 11
• B. 12
• C. 24
• D. 36

Answer 1

The Correct Option is A

Step 1: From the equation \( x + y = 23 \), we have:

\[ x + y = 23 \Rightarrow x = 23 - y \] 

Step 2: Substituting \( x = 23 - y \) into \( x^2 - y^2 = 23 \):

\[ (23 - y)^2 - y^2 = 23 \]

Step 3: Expanding the equation:

\[ (529 - 46y + y^2) - y^2 = 23 \Rightarrow 529 - 46y = 23 \]

Step 4: Solving for \( y \):

\[ 529 - 23 = 46y \Rightarrow 506 = 46y \]

\[ y = \frac{506}{46} = 11 \]