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

Max E.

Degree: Maths (Masters) - Bath University

Subjects offered: Maths


“About Me: I am Maths student at the University of Bath. I am a fun, easy-going individual with a real passion for numbers and all things mathematical. I have plenty of teaching experience having tutored pupils and helped in schools fo...”

MyTutor guarantee

£18 /hr

Luke C.

Degree: Physics with Astronomy (Masters) - Nottingham University

Subjects offered: Maths, Physics


“I'm a physics student at the University of Nottingham. I'm looking forward to tutoring people who have a similar passion for my subject.”

MyTutor guarantee

£18 /hr

Kate G.

Degree: Biochemistry (Bachelors) - Exeter University

Subjects offered: Maths


“Hello everyone, I'm Kate and I'm currently in my first year studying Biochemistry at the University of Exeter. I am a member of the canoeing society and enjoy taking part in the training sessions they have on offer. I have had previou...”

MyTutor guarantee

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

How do I expand (x+a)(x+b)? (plus example)

Find the values of a, b and c in the equation: (5x + 3)(ax + b) = 10x^2 + 11x + c.

Factorise and solve x^2 – 8x + 15 = 0

How Would I Factorise A Quadratic Equation?

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