How do I solve a pair of simultaneous equations?

An example of a pair of simultaneous equations is as follows:

4x + 3y = 10        (1)   and

2x - 3y = 14         (2)

Now to solve these equations we can simply add them and solve for x, then sub that value of x in to one of the original equations and solve for y, but how and why do we do that?

Firstly we can try to eliminate one of the unknowns from equation (1) by using equation (2), in this case we can simply add them to eliminate y. So upon adding (1) and (2), we are left with:

6x = 24        (3)

As you can see, upon adding 3y to -3y, the unknown y has been taken out of the equation all together, which now allows us to find a value for x. Now dividing both sides of (3) by 6, we are left with:

x = 4

Hooray, we've manipulated our two equations and managed to find a value for x, now how can we find y?

To find the value of y, we can simply put our newly found value of x back in to (1). So lets try that and see what we get:

4(4) + 3y = 10, which can also be written as:

16 + 3y = 10       (4)

So now we can take the 16 from both sides of (4) which gives us:

3y = -6

Now dividing through by 3 we are left with:

y = -2

Hooray! So by using the two equations we were originally given and manipulating them in a certain way, we have solved them and found the values of the unknown variables x and y.

Reece K. A Level Maths tutor, GCSE Maths tutor, A Level Physics tutor...

12 months ago

Answered by Reece, a GCSE Maths tutor with MyTutor

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


George S. GCSE Further Mathematics  tutor, A Level Further Mathematic...
View profile
£18 /hr

George S.

Degree: Physics (Masters) - Birmingham University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“About Me: I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe...”

MyTutor guarantee

Venetia L. A Level Maths tutor, GCSE Maths tutor, A Level Further Mat...
View profile
£20 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About Me: I study General Engineering at the University of Durham. I have always enjoyed the maths and science subjects, and hope to help students who also share my love for them too! I have experience in working with young pupils and...”

Charlie N. GCSE Economics tutor, IB Economics tutor, A Level Economic...
View profile
£18 /hr

Charlie N.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Philosophy+ 1 more


“About Me I am currently studying economics at the University of Bristol, a subject I have always been passionate about. From a younger age it always interested me and being able to study it first at A level and now at degree level, ...”

MyTutor guarantee

About the author

Reece K. A Level Maths tutor, GCSE Maths tutor, A Level Physics tutor...
View profile

Reece K.

Currently unavailable: for new students

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered: Maths, Science+ 4 more


“Who am I?My name is Reece, I'm 21 and I study Aerospace Engineering at the University of Bristol. I've just finished my 3rd year and am about to embark on a year in industry with Airbus, working in Flight Physics, before returning to...”

You may also like...

Other GCSE Maths questions

Solve the equation:

A table has diameter 130cm. What is the area, as a multiple of Pi

Simplify the expression: 3x + 2y -7x + c + y

How do I solve the Hannahs sweets question from the 2015 GCSE paper?

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss