Solve: \(x+y=x^2-y^2=23\) find \(y\)
- 11
- 12
- 24
- 36
The Correct Option is A
Solution and Explanation
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 \( y \):
\[ 529 - 23 = 46y \Rightarrow 506 = 46y \]
\[ y = \frac{506}{46} = 11 \]
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