Solve the simultaneous equation: 6x+y = 27 3x-2y = 6

To work out simultaneous equations, the aim is to remove one letter from the equations, i.e. Remove the y's so you have only x's and numbers (or vice versa).

One way to do this is to get the coefficient in front of either the y's or x's to equal each other.

In this example, you can get the coefficients of the x's to equal each other if you multiply the second equation by two:

3x-2y = 6    (x2)

=   6x-4y = 12

So now..

6x+y = 27

6x-4y = 12

Since the coefficients equal each other, you can take one equation away from the other to remove the x's:

6x+y = 27

6x-4y = 12


5y = 15           (y--4y = 5y, and 27-12 = 15)

Now solve y. 

y = 15/5

y= 3

Now to find what x is, you put 3 in as y to either of the original equations:

6x+y = 27

6x+3 = 27

6x = 24

x = 4

There you go! 

x=4 and y=3

to check you have the correct values, you can put the numbers back into the other equations. If the equation works you have it right.

3x-2y = 6

12-6 = 6

It works! 

Emily B. GCSE Maths tutor, GCSE Biology tutor, GCSE Chemistry tutor, ...

2 years ago

Answered by Emily, a GCSE Maths tutor with MyTutor

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


£18 /hr

Kamil F.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

£30 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:Maths, Physics+ 3 more

-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

£22 /hr

Raquel L.

Degree: Physics with Theoretical Physics (Masters) - Kings, London University

Subjects offered:Maths, Spanish+ 1 more


“I am a Physics with Theoretical Physics student at King´s College London. And if there is something that I love even more than Physics and Science is learning. I love it so much that I decided to leave my country, leaving there my fam...”

About the author

Emily B.

Currently unavailable: for regular students

Degree: Medicine (Doctorate) - Durham University

Subjects offered:Maths, Chemistry+ 2 more

-Medical School Preparation-

“Hi! I'm Emily, a second year medical student at Durham University. I am happy to help your child with Maths GCSE and AS-Level, Biology, Chemistry and Geography GCSE and A-Level and medical school applications. I have achieved an A* in...”

MyTutor guarantee

You may also like...

Posts by Emily

Describe adaptations of plants that live in dry conditions, such as the desert.

Solve the simultaneous equation: 6x+y = 27 3x-2y = 6

What is the mass (g) of 0.25mols of NaCl?

Other GCSE Maths questions

Solve the equation 4x + 2 = -5x + 20

A gym has 275 members. 40% are bronze members. 28% are silver members. The rest are gold members. Work out the number of gold members.

Solve the quadratic 3x^2+11x+6=0

Solve: 3(x - 2) = 21

View GCSE Maths tutors

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