Question:
Solve the system of equations: \(x + y = 3\), \(x - y = 1\).
Solve the system of equations: \(x + y = 3\), \(x - y = 1\).
Show Hint
Use addition or subtraction to eliminate one variable in a system of linear equations.
Updated On: Jan 13, 2026
- \(x = 1, y = 2\)
- \(x = 2, y = 1\)
- \(x = 3, y = 0\)
- \(x = 0, y = 3\)
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The Correct Option is B
Solution and Explanation
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.
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