Solve the simultaneous equations 2x - y = 13, x - 2y = 11

1. In order to solve simultaneous equations, you need to make either terms of x (i.e. '2x') or terms of y (i.e. 'y') in equation (1) and equation (2) equal. To do this, multiply either (1) or (2) as shown below.

(1) 2x - y = 13     (x2)           =       (1) 4x - 2y = 26

(2) x - 2y = 11                               (2) x - 2y = 11 

2. Cancel out the alike terms (in this case, '2y') and follow the equation through. Important: remember the rules about adding and subtracting +s and -s. 

   (1) 4x - 2y = 26

-  (2) x - 2y = 11                        < (A minus and a minus equal a plus! In other words -2y - -2y = -2y + 2y = 0)

= 4x - x = 26 - 11

3x = 15

x = 5

3. Substitute your new value for x into one of the original equations and follow through.

x - 2y = 11  becomes  5 - 2y = 11

5 - 11 = 2y

• 6 = 2y

-3 = y

x = 5 and y = -3