2 Main PointsSolve two (or more) equations at the same time (simultaneously)Only one set of numbers will satisfy (work in) both equationsIf you set out your working carefully you can collect most of the marks even if your answer is incorrect
3 Rough Guide to solving sim. Equations. Always number your equations - this makes it easier to show your working.Take your time - these will be worth a lot of marks.No short-cuts.
4 The ‘Nuts and Bolts’You must have either the same number of x’s or y’s. - if not you will need to multiply one or more equations.Find either x or y by adding or subtracting and then substitute that value into one of the equations to find the other value.Always check your answers in the ‘remaining equation’
5 Same Sign Subtract Solve 2x + y = 8 and 5x + y = 17 - 3x + 0 = 9 x = 3 Substitute x = 3 in x 3 + y = 8 so y = 2Check in (not used directly to find y)5 x = 17 so x = 3 and y = 2122112
6 Different Signs Add Solve 3x + 2y = 8 x - 2y = 0 + 4x + 0 = 8 so x = 2 Substitute x = 2 in to find y3 x 2 + 2y = 8 so 2y = so y = 1Check in x 1 = 0So x = 2 and y = 1121212
7 Different amounts of x and y Solve x + 2y = 11and 3x + y = 18Need either same number of x’s or y’s so x3This gives 3x + 6y = 33(SSS) y = so y = 3Sub y = 3 in x + 2x3 = 11 so x = 5Check in x5 + 3 = 18 so x = 5 and y = 312133212