Answer the following simultaneous equation:

Equation 1) x+y2=5  (Equation 2) y=3x+1

The value of x is the same in both equations, as is the value of y. Therefore we can use one to work out the other. for example taking equation 1 and definining x in terms of y by rearranging the equation.



Equation 2 tells us what y is, so we can put that into equation 1 Therefore...

x2 + (3x+1)(3x+1) = 5

...then expand the brackets

x2 + 9x2 +3x +3x +1 = 5

...then group the factors

10x2 +6x +1 =5, then get the equation to equal 0 so we can factorise... 10x2 +6x -4 = 0


5x-2=0 or 2x+2=0

5x=-2 or 2x=-2

x=-2/5 or x=-1

we know that x=-1 as x and y are whole numbers in this equation. Therefore, to check this we put x back into the original equations to find out the value of y.

y=3x+1.... y=3(-1)+1..... y=-2

So put the values of x and y into equations 1 to check these values...

x2 +y2=5

(-1)2+ (-2)2=5

as 1 +4 =5

Now we know the values of x and y are corect

Jenn S. A Level Psychology tutor, GCSE Psychology tutor, A Level Hist...

1 year ago

Answered by Jenn, a GCSE Maths tutor with MyTutor

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


£20 /hr

Samuel A.

Degree: Medicine (Bachelors) - University College London University

Subjects offered:Maths, Chemistry+ 2 more

-Medical School Preparation-

“Hello I'm Samuel Aston and I'm a second year UCL medic looking for students needing help in attaining their full potential and the top marks!”

£18 /hr

Alexander R.

Degree: MSc Financial Analysis and Fund Management (Masters) - Exeter University

Subjects offered:Maths, Economics


“1st Class Economics Graduate and Postgraduate student with broad tutoring experience - let me help you achieve!”

Aimee K. A Level English tutor, IB English tutor, 13 Plus  English tu...
£30 /hr

Aimee K.

Degree: Ancient & Modern History (Bachelors) - Oxford, Magdalen College University

Subjects offered:Maths, History+ 8 more

Extended Project Qualification
English and World Literature
English Literature
Classical Civilisation
-Personal Statements-
-Oxbridge Preparation-

“Hey there! I am an Ancient & Modern History student at Magdalen College, Oxford University and I absolutely love history and studies to do with culture and literature.  I am a big believer in providing students with the best groundin...”

About the author

£18 /hr

Jenn S.

Degree: Psychology (Bachelors) - Birmingham University

Subjects offered:Maths, Psychology


“I am studying Psychology at Birmingham University. I have always thoroughly enjoyed learning a wide range of subjects especially maths, psychology and history and have a passion in encouraging others to learn to love education too. I ...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Solve the simultaneous equations: 4x+3y=5 and x-y=3, to find the values of x and y.

Surd Calculations?

How do I solve a quadratic equation by factorising?

How to solve a simple simultaneous equation

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