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...

5 months ago

Answered by Jenn, a GCSE Maths tutor with MyTutor

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


£18 /hr

James B.

Degree: Mathematics (Masters) - Exeter University

Subjects offered: Maths


“About MeI'm a second year student at Exeter University. I've been passionate about maths from a young age and have carried that love through my school and uni career. I hope that I can generate the same passion for my tutees as well....”

£18 /hr

Jill M.

Degree: Modern Languages and Cultures (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 2 more


“I'm in my second year at Durham University studying French and Spanish. I love languages and am eager to help you with your French or Spanish studies in any way that I can!”

£18 /hr

Jan K.

Degree: Mathematics and Music (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics


“About Myself I am a Mathematics student at Edinburgh University. I have a real passion for Mathematics, and I thouroughly enjoy explaining mathematical concepts to others. Having been home-educated all through school (which also gave ...”

MyTutor guarantee

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 5x - 7 = 3x + 2, to find the value of x

How do i solve a system of 2 equations?

How do I factorise x^2 ​- 4?

Bag A contains £7.20 in 20p coins. Bag B contains only 5p coins. The number of coins in bag B is three-quarters of the number of coins in bag A. How much money is in bag B?

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