Treat this as a pair of simultaneous linear equations. A reliable method is elimination: choose one variable, multiply the equations if needed, and add or subtract so that one variable disappears. Solving the system gives x and y values that satisfy both equations at the same time. Here the solution is x=7, y=-4. We should verify it, not just stop after solving: substituting the ordered values into 5x + 1y = 31 and 3x + 4y = 5 makes both equations true. That confirmation shows the selected answer is correct.