How do i solve simultaneous equations?

simulatneous equations are solved by eliminating one of the unknowns such as x or y. there are a number of ways to do this such as substitution or subtraction/addition. For this example we will use subtraction addition as i always found that the easier method at GCSE since it often avoids fractions.

e.g. 2y=3x+12 and 3y=5x+14

we need to choose one of the two unknowns to eliminate and then find their lowest common denominator. I will choose x, where the LCD is 15 (3*5=15). now we multiply the entire equation through in order that the number in front of x (called the coefficient) is 15. in the first equation, we multiply through by 5.



in the second equation we multiply through by 3 like before



now both the coefficients of x are 15 so we can subtract one equation from the other




we now have the y value, since x is now zero. to find the x value all we need to do is go back to one of the first equations and put the value y=18 into the equation to resolve for x.





and thats everything. By making sure we can subtract one equation from another to eliminate one of the unkowns we can subsequently obtain both values. in this case, y=18 and x=8 

Matthew K. GCSE Maths tutor, GCSE Physics tutor

1 year ago

Answered by Matthew, a GCSE Maths tutor with MyTutor

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


Ben W. GCSE English tutor, GCSE Philosophy tutor, A Level Philosophy ...
View profile
£18 /hr

Ben W.

Degree: Philosophy, Politics and Economics (Bachelors) - Durham University

Subjects offered: Maths, English+ 2 more

.TSA. Oxford.
-Personal Statements-

“Hi, I'm Ben and I study Philosophy, Politics and Economics (PPE) at Durham University! I have fostered ambitions to become a teacher for sometime now and would love the chance to work with you to try and get the best out of your acade...”

MyTutor guarantee

Tom V. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor, A L...
View profile
£18 /hr

Tom V.

Degree: Mechanical Engineering (Masters) - Leeds University

Subjects offered: Maths, Physics


“About MeHello! I'm Tom, I'm in my first year studying mechanical engineering at the University of Leeds. I've always loved sicence, being particularly drawn to physics and maths from a young age. I loved the methodical, logical appro...”

MyTutor guarantee

Aidan T. GCSE Maths tutor, A Level Maths tutor
View profile
£20 /hr

Aidan T.

Degree: Chemical Engineering (Masters) - Edinburgh University

Subjects offered: Maths


“Hi! I am currently studying Chemical Engineering at The University of Edinburgh. I tutor in Edinburgh 6-7 times per week currently, and joined MyTutor as a way of sumplimenting that with the convenience of being able to stay in my ...”

About the author

PremiumMatthew K. GCSE Maths tutor, GCSE Physics tutor
View profile
£22 /hr

Matthew K.

Degree: General Engineering (Masters) - Warwick University

Subjects offered: Maths, Physics


“About MeI am a student studying a general engineering masters degree at Warwick University. I amfun and friendly and have a passion for maths and physics with a little bit of rugby on the side.I helped my brother whilst he was ...”

You may also like...

Posts by Matthew

How do I find the coordinates of maximum and minimum turning points of a cubic equation?

How do i solve simultaneous equations?

How to i calculate total resistance in a circuit?

Other GCSE Maths questions

How do I simplify the equation 4x + 5x -2 - 2x + 7?

How do I find the equation of a line connecting points a(p,q) and b(r,s)?

Why maths?

How to expand brackets?

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