831 views

### What is solution by substitution?

Simultaneous equations - Solution by substitution

As the variables (x & y) are the same in both equations, we can substitute from one equation into the other. This will give an equation with just one variable, which can easily be solved.

Example:

Equation 1   3y = 6x - 3

Equation 2   4y = 5x + 2

Make y the subject of equation 1, then substitute into equation 2:

·         Equation 1, divide both sides by 3 gives    y = 2x – 1

·         Equation 2, substitute for y from above gives  4(2x – 1) = 5x + 2

·         Multiply out brackets         8x – 4 = 5x + 2

·         Simplify and solve             3x = 6  therefore   x = 2

Substitute this value back into either of the original equations to solve for y:

Equation 1    3y = 6 (2) -3  therefore y = 3.

Key tip: Instead you could have made x the subject of an equation, and it can be either equation. Before you begin, think carefully about which variable will be easiest to make the subject of which equation.

2 years ago

Answered by Antonia, who tutored GCSE Maths with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 780 SUBJECT SPECIALISTS

£36 /hr

Degree: Philosophy, Politics and Economics (Bachelors) - Oxford, Oriel College University

Subjects offered:Maths, English+ 3 more

Maths
English
Economics
.TSA. Oxford.
-Oxbridge Preparation-

“University of Oxford and University of Chicago educated tutor - looking to help students reach their full potential in an engaging and effective way.”

£24 /hr

Degree: Bioscience (Masters) - Durham University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Human Biology
English
Chemistry
-Personal Statements-

“Hi! I'm Steven and studying Biomedical Science at Durham. I'm friendly, approachable, and passionate for my subjects.”

£24 /hr

Degree: Dentistry (Bachelors) - Kings, London University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Psychology
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi, my name is Karolina and I am a Dentistry Student from King's College London.  I understand that many students find certain aspects of the A-level syllabus challenging and having recently completed mine I believe that I know how to...”

Currently unavailable: for new students

Degree: Chemistry (physical natural sciences) (Masters) - Cambridge alumni University

Subjects offered:Maths, Science+ 1 more

Maths
Science
Chemistry

“Science and Maths tutor from the University of Cambridge, keen to support you in getting top grades.”

### You may also like...

#### Posts by Antonia

How do you calculate work done?

What is Le Chatelier's Principle?

What is solution by substitution?

#### Other GCSE Maths questions

Show that n²-n-90=0

Solve x² + x -12

What is Standard form? And when can I use it?

Write 825 as a product of its prime factors.

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.