Solve the system of equations: 2x + y = 12, 7x - 2y = 31

Multiply the first equation by 2: 4x + 2y = 24.

Add this to the second equation: (4x + 2y) + (7x - 2y) = 24 + 31, which simplifies to 11x = 55, so x = 5.

Substitute x = 5 into the first equation: 2(5) + y = 12, so 10 + y = 12, which means y = 2.

Solution: x = 5, y = 2.