I’ve been taught two methods for solving pairs of simultaneous equations. When should I use which?

You’ve been taught elimination and substitution. (You should also be able to solve simultaneous equations graphically.) In the elimination method, you multiply up the equations to make them have a term that ‘matches’. Then you add or subtract the equations from one another to eliminate the variable in the term that matches. This tends in many cases to be the more efficient way of solving linear simultaneous equations, such as 5x + 7y = 19 and 3x + 2y = 7.

In the substitution method, you make a variable the subject of one equation, then substitute the expression you’ve found for that variable into the other equation. This good for linear simultaneous equations when your question is close to giving you one variable as the subject. For example, in x + 2y = 13 and 3x + 7y = 44 we’re one step away from the first equation having x as the subject. However, you can see that in the first example, 5x + 7y = 19 and 3x + 2y = 7, we’d end up with much more complicated algebra than by the elimination method. The time when you really must use substitution is when one of the equations is linear and the other is non-linear, e.g. 3x + y = 7 and xy + x^2 = 6. An equation is non-linear, roughly speaking, if it has two variables multiplying one another, or a variable raised to a different power than 1. We usually rearrange the linear equation to make one variable the subject, then substitute into the non-linear equation. To sum up, substitution works in all the cases you’ll encounter, while elimination only works for linear cases, but elimination tends to make life easier when it works. So if it looks linear, use elimination, but if it looks non-linear (or you’re really confident you can isolate one variable easily) use substitution. 

RM
Answered by Rosemary M. Maths tutor

6592 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Jorgen has 20 sweets in his pocket. The sweets are either blue or yellow. He picks a sweet and eats it and takes another sweet and eats it again. The probability of him picking two blue sweets is 6/30. How many yellow sweets does he have in his pocket.


Solve the following simultaneous equation: y= x^2 - 3x + 4 y - x = 1


Express 0.545454... as a fraction in its simplest form.


Solve the following equation : x^2 + 2x +1 = 0


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences