how do you solve these simultaneous equations?

6x + y = 8 (1)       4x - y = 12 (2)


Method 1 elimination:

-Adding/subtracting the two equations together to eliminate one of the unknowns 

 (1) + (2)

  6x + y = 8

+  4x - y = 12

10x = 20        (/10)

x= 2

sub 'x=2' into (2)

4(2) - y = 12

8 - y = 12      (+y) 

8 = 12 + y     (-12)

-4 = y

Method 2 substitution:

-rearranging one of the equations to make an unknown the subject 

rearrange (2)

4x - y = 12 

4x = y + 12      (+y)

y= 4x - 12        (-12)

sub 'y = 4x - 12' into (1)

6x + '4x - 12' = 8

10x - 12 = 8        (+12)

10x = 20

x = 2

sub 'x=2' into 'y = 4x - 12'

y = 4(2) - 12 

y = 8 - 12

y = -4

Shriya G. GCSE Maths tutor, A Level Maths tutor, GCSE Chemistry tutor...

1 year ago

Answered by Shriya, who has applied to tutor GCSE Maths with MyTutor

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


£18 /hr

Celine A.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Hello! I'm Celine and I am currently in my second year of my Maths degree at the University of Bristol.  I offer any level of Maths tutoring up to and including Maths and Further Maths A-level.  We can go through your course and home...”

MyTutor guarantee

£18 /hr

Mohammad M.

Degree: General Engineering (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 2 more


“I am studying Engineering at Durham University. From a very early age I have been fascinated by machines; how they work, how they have developed over time, and how they are useful in society today. I have a keen interest in motors and ...”

MyTutor guarantee

£22 /hr

Maddy M.

Degree: Psychology (Bachelors) - Exeter University

Subjects offered: Maths, Sociology+ 2 more

-Personal Statements-

“About Me: I am currently studying Psychology at the University of Exeter having had a realpassion for it from the age of 15. Psychology is a vast and ever-evolving science, aspects which fuel my interest for it. My own interests with...”

About the author

£18 /hr

Shriya G.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths, Chemistry


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How do I remember the area of a circle if it's not in the formula book?

Where does the quadratic equation come from?

How do I find the equation of a straight line?

How do I differentiate?

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