Solve the simultaneous equations 2x + 3y = 4, 3x + 6y = 3

Label the equations
(1): 2x + 3y = 4
(2): 3x + 6y = 3

We need the same number of x's or y's in the equations, so multiply (1) by 3 and (2) by 2
giving (3): 6x + 9y = 12
(4): 6x + 12y = 6

Subtract (3) from (4)
6x + 12y - 6x - 9y = 6 - 12
so 3y= -6
so y= -2

Substitute the y value into (1) to find x
2x + (3*-2) = 4
        2x - 6 = 4
             2x = 10
               x = 5

Check by substituting into (2)
(3*5) + (6*-2) = 15 - 12 = 3 the solutions work

So x = 5 and y = -2

Sophie S. GCSE Biology tutor, GCSE Chemistry tutor, GCSE Physics tuto...

1 year ago

Answered by Sophie, a GCSE Maths tutor with MyTutor

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


£22 /hr

Shannon W.

Degree: Chemistry with Medicinal Chemistry (Masters) - Newcastle University

Subjects offered:Maths, Science+ 3 more

-Personal Statements-

“About me: I am a chemistry student at Newcastle University. I have always been interested in science and mathematics, and can sit for hours watching documentaries on the subjects. I really enjoy getting stuck into exam questions and ...”

£24 /hr

Daniel R.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“About me I’m a first year student studying Maths with European Studies at Durham. I have recently taken my A levels, achieving A* in Maths and Further Maths, so I am familiar with the course content and what the examiners are looking ...”

£18 /hr

Oscar G.

Degree: Economics and Politics (Bachelors) - Bristol University

Subjects offered:Maths, Politics+ 1 more


“About Me: I am a Economics and Politics student at Bristol University. I have always had a real passion and love for all things involving Mathematics, Economics and Politics and hope that my tutorials will instill that love in you, to...”

MyTutor guarantee

About the author

Sophie S.

Currently unavailable: for new students

Degree: Biochemistry (MBiochem) (Masters) - St. Andrews University

Subjects offered:Maths, Science+ 3 more


“About me: Hello, I’m Sophie and I’m in first year at the University of St Andrews, studying for a biochemistry integrated masters. I haveprevious experience at tutoring as I tutored a family friend inall three sciences for her GCSEs. ...”

You may also like...

Posts by Sophie

Describe the reflex arc.

Solve the quadratic equation x^2 + 3x + 2 = 0, by factorisation.

Solve the simultaneous equations 2x + 3y = 4, 3x + 6y = 3

What is a metabolic rate?

Other GCSE Maths questions

Why is anything to the power 0 equal 1?

Solve the following simultaneous equations: 2a-5b=11, 3a+2b=7

Solve the simultaneous equations x^2 + y^2 = 9 and x+ y = 2. Give your answer to 2.d.p

How do I do the dot product with vectors?

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