How do you solve a simultaneous equation?

Example question:

Solving Simultaneous Equations

Equation 1: 6x + 2y = 2
Equation 2: 5x - 7y = 6.
Find x and y.

1) Check is if it is possible to solve. Here we have 2 unknowns, x and y, and 2 equations, therefore it is possible to solve. (If there are more unknowns than equations then it is not possible to solve.)

2) Eliminate an unknown in one of the equations.

- Rearrange each equation to get the x terms on one side and the y terms on the other.

Eq 1 .... 6x=2-2y
Eq 2 .... 5x=6+7y

- Look for a common multiple for the coefficients (number in front of the unknown) of x, e.g. 30. So we multiply each equation up to get 30x on one side, then we can say equation 1 equals equation 2.

5 x Eq 1 .... 30x=10-10y .... we will call this Eq 3
6 x Eq 2 .... 30x=36+42y .... we will call this Eq 4

- Remember what you do to one side of the equation you must do to the other.

3) Now both Eq3 and Eq4 are of the form 30x=.... we can say that Eq3=Eq4.

10-10y = 36+42y

4) Now just solve as you would normally to find y=-0.5.

5) Put this value of y into Eq1 to find x=0.5.

6) Put both these values into Eq2 to check result, e.g. 60.5 + 2-0.5 = 3 - 1 = 2.
This is correct therefore we have the correct answer.

TF
Answered by Toby F. Maths tutor

5791 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

work out: ( 4 × 10^3 )^2 + 3.5 × 10^7 and give your answer in standard form.


Jo wants to work out the solutions of x^2 + 3x – 5 = 0. Can the solution be worked out?


White paint costs £2.80 per litre. Blue paint costs £3.50 per litre. White paint and blue paint are mixed in the ratio 3 : 2 Work out the cost of 18 litres of the mixture.


A is the point (4,1). B is the point (10,15). Find the perpendicular bisector or of AB.


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning