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 ...

1 year 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

Javed R.

Degree: Biomedical Engineering (Bachelors) - Liverpool University

Subjects offered:Maths, Chemistry


“Postgraduate Biomedical Engineering student at the University of Strathclyde. Past classroom experience.”

£18 /hr

Dan W.

Degree: Economics and Accounting (Bachelors) - Bristol University

Subjects offered:Maths, Economics


“I achieved top grades whilst juggling cricket at a high level. I’ve tutored for Young Einstein Tuition & been a Peer Mentor to those facing personal issues”

£22 /hr

Lucy B.

Degree: Anthropology (Doctorate) - Cambridge University

Subjects offered:Maths, Science+ 5 more

-Personal Statements-
-Oxbridge Preparation-

“Enthusiastic Cambridge grad, with experience in Biology and Maths, passionate about helping students reach their potential and achieve the grades they deserve. ”

MyTutor guarantee

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 I know how many solutions a quadratic equation has?

What is algebra used for?

Insert one pair of brackets so that this calculation is correct; 3 x 6 + 5 - 1 = 32

Rearrange y = (3x+5)/x to make x the subject

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