How do i solve a system of 2 equations?

This problem is one that can be confusing if not tackled orderly. Let us have an example of a system of 2 equation:

3x + 5y = 13

4x + 7y = 18

First we must choose one of the two and then express one of our variables with respect to the other. Let's take the first one and express with respect to x:

3x + 5y = 13

5y = 13 - 3x

y = 13/5 - 3x/5

Already it doesn't look very nice, but do not panic! the next step is to use this formula for the next equation. By substituting y in the second equation with this function of x we will have a single equation with only x as an unknown:

4x + 7y = 18

4x + 7*(13/5 - 3x/5) = 18

Now we group the x factors toghether:

4x + 7*13/5 - 7*3 x/5 =18

(4 - 7*3/5)*x + 7*13/5 =18

We put the constants on the right hand side and divide the whole equation by the x factor.

(4 - 21/5)*x = 18 - 7*13/5

x = (18 - 91/5) / (4 -21/5)

Now it all comes down to a simple calculation for the numerator and denominator.

numerator = (18*5-91)/5 = -1/5

denominator = (4*5-21)/5 = -1/5

In this case they are equal, so we find x

x = 1

Now we substiture this result in the first equation and we can find the last unknown, y

3x + 5y = 13

3*1 +5y = 13

5y = 13-3

5y = 10

y = 2

The answers are x=1 and y=2. This is the simplest way to solve the 2 equation system and it work for any system. There are some methods that can solve system of more than 2 equations, but that is a topic for another time.

Ioan I. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor, A ...

6 months ago

Answered by Ioan, a GCSE Maths tutor with MyTutor

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


£18 /hr

Shona S.

Degree: Economics (Bachelors) - Birmingham University

Subjects offered: Maths, Economics+ 1 more


“I am a second year Economics student, studying at University of Birmingham. At school I studied Economics, Maths and Biology for A levels and having enjoyed learning them, so I feel I will be able to enthusiastically teach these subje...”

£18 /hr

Jacob M.

Degree: History (Bachelors) - Manchester University

Subjects offered: Maths, History+ 1 more


“Tutoring experience I have gained three years tutoring experience with five seperate students of different ages and capabilities on a one-to-one basis. The subjects I have tutored include Maths, Biology, Physics and Chemistry at GCSE ...”

£20 /hr

Lloyd S.

Degree: Mathematics G100 (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About Me:I am 19 and from Devon, currently in my first year studying Maths at the University of Bristol. I have a real passion for Maths and I really hope I can help you to understand, and maybe even enjoy doing maths - I know not ev...”

About the author

£18 /hr

Ioan I.

Degree: Natural Sciences 1 (Bachelors) - Cambridge University

Subjects offered: Maths, Physics


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

MyTutor guarantee

You may also like...

Posts by Ioan

How do i solve a system of 2 equations?

How do I solve this problem?

Other GCSE Maths questions

How do you solve this problem?

Find the equation of the line passing through the point ( 2, −3) which is parallel to the line with equation y + 4x = 7

How do I calculate the gradient of a linear (straight) graph?

Can you solve these simultaneous equations and find the values of x and y? Equation 1: 2x + y = 14 Equation 2: 4x - y = 10.

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