What is the solution of the equations (x+y=5) and (x-y=1)?

Correct answer: (x=3,\ y=2)

The direct answer is option A: \((x,y)=(3,2)\). Add the equations \(x+y=5\) and \(x-y=1\). The \(y\) terms cancel: \(2x=6\), so \(x=3\). Substitute into \(x+y=5\): \(3+y=5\), hence \(y=2\). Option A satisfies both equations: \(3+2=5\) and \(3-2=1\). Option B, \((2,3)\), gives sum 5 but difference \(-1\), not 1. Option C, \((4,1)\), gives sum 5 but difference 3. Option D, \((1,4)\), gives sum 5 but difference \(-3\). Thus checking both original equations confirms A. When coefficients of one variable are opposites, addition is usually the quickest elimination method.