Solve by substitution: (x+y=7) and (x-y=1). What is ((x,y))?

Correct answer: ( (4,3) )

The direct answer is option A: \((x,y)=(4,3)\). Using substitution, from \(x-y=1\) we get \(x=y+1\). Put this into \(x+y=7\): \((y+1)+y=7\), so \(2y+1=7\), \(2y=6\), and \(y=3\). Then \(x=y+1=4\). Option A works because \(4+3=7\) and \(4-3=1\). Option B, \((3,4)\), gives sum 7 but difference \(-1\). Option C, \((5,2)\), gives sum 7 but difference 3. Option D, \((2,5)\), gives sum 7 but difference \(-3\). The substitution idea is to express one variable in terms of the other, replace it in the second equation, and then back-substitute. Always check both original equations to catch sign errors.