Solving Pair of Linear Equations

Video Explanation

Question

If \(x = a,\; y = b\) is the solution of the system \(x – y = 2\) and \(x + y = 4\), find the values of \(a\) and \(b\).

Solution

Step 1: Given 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

Put \(x = 3\) in (2):

\[ 3 + y = 4 \Rightarrow y = 1 \]

Step 4: Identify Values

\[ a = 3,\quad b = 1 \]

Final Answer

\[ (a, b) = (3, 1) \]