Solve the simultaneous equations: x + 2y = 13, 4x - 3y = 8.

Multiply both sides of the equation x + 2y = 13 by 4 to get 4x + 8y = 52. Subtract 4x - 3y = 8 from 4x + 8y = 52 to get 11y = 44. Divide both sides of 11y = 44 by 11 to get y = 4. Since we now know y = 4, we can replace y with 4 in the equation x + 2y = 13 to get x + 8 = 13. Rearranging that to make x the subject of the formula results in x = 13 - 8 = 5, therefore the solution to the equations are x = 5, y = 4.