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.

 

Answered by Antonia M. Maths tutor

4743 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Given that 346 × 27 = 9342 , work out 34.6 × 2.7


Factorise: 6x^2-3x-3=0


How do you know when to use sin, cos and tan in trigonometry?


What is the best way to solve simultaneous equations?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy