Solve the simultaneous equations: 4x + y = 25, x - 3y = 16

We need to have either the same number of x's or the same number of y's in each equation so that we can add or subtract them to be left with just x or just y. We can do this by multiplying the second equation by 4:

4x - 12y = 64

Now both equations have "4x" in them, so if we subtract one from the other we will get rid of the x's and be left with just y's.

                4x + y = 25

MINUS     4x - 12y = 64

EQUALS         13y = -39

We then divide both sides of the equation to find what y equals:

y = -39/13 = -3

Now we substitute our value for y back into one of the equations to find what x is.

x - 3(-3) = 16

x + 9 = 16

x = 16 - 9 = 7

We can check our answers by substituting both the x and y values into the two equations. If the equations both balance then our answers are correct!

Lydia H. GCSE Maths tutor, IB Economics tutor

1 year ago

Answered by Lydia, who tutored GCSE Maths with MyTutor

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


£18 /hr

James T.

Degree: Economics & Management (Bachelors) - Bristol University

Subjects offered: Maths, Economics


“I am currently studying Economics & Management at the University of Bristol, and love working with students of all ages, specialising in Maths and Economics at both A-Level and GCSE. I have been teaching drums and coaching tennis for ...”

MyTutor guarantee

£18 /hr

Steven K.

Degree: Material Science (Masters) - Oxford, The Queen's College University

Subjects offered: Maths, -Personal Statements-

-Personal Statements-

“I started tutoring through my father who is a maths teacher, as he would pass on requests for lessons to me. Through my A levels I tutored GCSE maths, and began to also teach physics, chemistry and biology, the other subjects i was st...”

£20 /hr

Jonathan P.

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Physics


“About Me: I am a Physics student at Durham University. My passion is physics, and by association maths, I will aim to instil asimilar passion in students during my tutorials. I am a highly patient and approachable individual.  I have...”

About the author

Lydia H.

Currently unavailable: until 01/06/2016

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Economics


“I am a second year Economics student at Durham University with passion for maths and economics which I hope to instil in you! I love helping other people achieve their goals and first tutored over four years ago.My aim is to explain ...”

MyTutor guarantee

You may also like...

Posts by Lydia

Explain one reason why governments impose indirect taxes.

Solve the simultaneous equations: 4x + y = 25, x - 3y = 16

Other GCSE Maths questions

Solve 5x - 6 = 3x + 7

Solve the simultaneous equations: 5x + 3y = 9 and 7x - 2y = 25.

The first four terms of an arithmetic sequence are: 3, 10, 17, 24. What is an expression, in terms of n, for the nth term?

Rearrange the formula to make 'y' the subject: x = (1 - 2y)/(3 +4y)

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