Question

Solve the system of equations: \(x + y = 3\), \(x - y = 1\).

• A. \(x = 1, y = 2\)
• B. \(x = 2, y = 1\)
• C. \(x = 3, y = 0\)
• D. \(x = 0, y = 3\)

Hint:

Use addition or subtraction to eliminate one variable in a system of linear equations.

Answer 1

The Correct Option is B

Add the equations: \[ (x + y) + (x - y) = 3 + 1 \implies 2x = 4 \implies x = 2 \] Subtract the second from the first: \[ (x + y) - (x - y) = 3 - 1 \implies 2y = 2 \implies y = 1 \] Verify: For \(x = 2, y = 1\), \(2 + 1 = 3\) and \(2 - 1 = 1\), which satisfies both equations. Thus, option (2) is correct.