What is the solution of (7x+6y=5) and (5x-6y=31)?

Correct answer: \(x=3,\ y=-\frac{8}{3}\)

Adding the two equations gives \((7x+6y)+(5x-6y)=5+31\), so \(12x=36\). Hence, \(x=3\). Substituting this into \(7x+6y=5\) gives \(21+6y=5\), so \(6y=-16\) and \(y=-\frac{8}{3}\). Therefore, the solution is \(x=3,\ y=-\frac{8}{3}\). In option A, \(x=2\) would give \(12x=24\), not \(36\), after adding the equations. Exam tip: when coefficients of a variable are opposites, add the equations to eliminate that variable directly.