Finding Values of a and b
Video Explanation
Question
If \(x = a,\; y = b\) is the solution of the system \(x – y = 2\) and \(x + y = 4\), find \(a\) and \(b\).
Solution
Step 1: Write Equations
\[ x – y = 2 \quad (1) \]
\[ x + y = 4 \quad (2) \]
Step 2: Add Equations
\[ (x – y) + (x + y) = 2 + 4 \]
\[ 2x = 6 \Rightarrow x = 3 \]
Step 3: Substitute Value
Substitute \(x = 3\) in (2):
\[ 3 + y = 4 \Rightarrow y = 1 \]
Step 4: Final Values
\[ a = 3,\quad b = 1 \]
Final Answer
\[ (a, b) = (3, 1) \]