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