11. If \(x = a\), \(y = b\) is the solution of \(x - y = 2\) and \(x + y = 4\), then \(a\), \(b\) are, respectively
3 and 5
5 and 3
3 and 1
–1 and –3
Step 1: We are given the two equations:
\(x - y = 2\) ...(i)
\(x + y = 4\) ...(ii)
Step 2: Add equations (i) and (ii):
\((x - y) + (x + y) = 2 + 4\)
\(2x = 6\)
\(x = 3\)
Step 3: Substitute \(x = 3\) into equation (i):
\(3 - y = 2\)
\(-y = 2 - 3 = -1\)
\(y = 1\)
Step 4: Thus, the solution is:
\(a = 3\), \(b = 1\)
Final Answer: Option (C) — 3 and 1.