Solve these simultaneous equations: 2x + 3y = 19 and x + 4y = 17.

By multiplying everything in equation 2 by 2, you get 2x + 8y = 34. If you then subtract equation 1 from this you get 5y = 15. Thus y = 3, going back to equation two, and subbing y back in, x + 12 = 17, therefore x = 5.