solve the following for x and y 1/3x + 1/2 y = 6 1/2x - 1/2y = -1

To solve for x and y, we can use the method of elimination or substitution. Method of elimination: We can multiply the first equation by 2 and the second equation by 3 to obtain two equations with the same coefficients for x and y: 2 * (1/3x + 1/2 y = 6) = 2/3x + y = 12 3 * (1/2x - 1/2y = -1) = 3/2x - 3/2y = -3 Now, we can subtract the second equation from the first equation to eliminate the y term: 2/3x + y = 12 (3/2x - 3/2y = -3) 1/6x + 2y = 15 Solving for y, we get: y = (15 - 1/6x) / 2 Substituting this expression for y in one of the original equations, we can solve for x: 1/3x + 1/2 (15 - 1/6x) / 2 = 6 Multiplying through by 6 and simplifying, we get: 2x + 9 - 1/3x = 36 5/3x = 27 x = 27 * 3 / 5 = 16.2 Finally, we can use the expression we found for y to find y: y = (15 - 1/6x) / 2 = (15 - 1/6 * 16.2) / 2 = 8.8 So the solution to the system of equations is (x, y) = (16.2, 8.8).