Simultaneous Equations starter 2x + y = 3 and 3x + y = 5 2x + y = 3 3x + y = 5 The y coefficient of both equations is 1 so eliminate y subtract 2x – 3x = 3 - 5 -x = -2 x = 2 In both equations the sign of y is the same so subtract 2x + y = 3 2(2) + y = 3 so 4 + y = 3 so y = 3 - 4 So y = -1 Ans x = 2, y = -1

Simultaneous Equations The coefficients must be equal so 2x + 3y = 7 x – y = 1 Multiply the second equation by 2 to get rid of the x OR 2x + 3y = 7 2x – 2y = 2 Multiply the second equation by 3 to get rid of the y The coefficients of x are both 2 so get rid of the x. 3y – -2y = 7-2 3y + 2y = 7-2 As the signs in front of x are both the same (+) then subtract 5y = 5 Solve for the remaining letter (in this case y) y = 1

Take one of the original equations x – y = 1 x – 1 = 1 Replace the letter you have found by its value x = 2 Ans x = 2 y = 1 Remember when you add or subtract you should only have 1 letter (variable) left