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.

 

AM
Answered by Antonia M. Maths tutor

5641 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Simplify fully (y+3)^2


In a sale the price of a shirt is reduced by 60%. The sale price is £7.98. What is the original price?


The equation of line L is y = 3x - 2 and the equation of line Q is 3y - 9x + 5 = 0, show these two lines are parallel


There are 10 boys and 20 girls in a class. In a class test, the mean score of the boys is 77. The mean score of the girls is 80. What is the mean score of the whole class?


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences