How can we solve a two-equation, two-unknown values?

If we have two equations that look like this:

a1 * x + b1 * y = c1


a2 * x + b2 * y = c2

where x,y are variables and a1,a2,b1,b2 are coeficients.

then we solve it using the following method:

We choose either x or y and we try to reduce their coeficients so that either a1=a2  or b1=b2. If we make one of these possible, then we can reduce one of the variables and we are left with the other. Let's assume that we have a1=a2=a. Then:

a * x + b1 * y = c1

a * x + b2 * y = c2

We can reduce the two equations and we are left with:

(b1-b2) * y = c1 - c2

From here we can find y as we know the values of b1,b2,c1 and c2. After that, we replace y in one of the equations and we deduce x.

If a1 was different from a2, then we would've had to multiply the equations so that we can make those two equal.

Thus, we have solved a two-equation, two-unknown values system.

Cosmin B. A Level Maths tutor, GCSE Maths tutor, GCSE Computing tutor...

2 years ago

Answered by Cosmin, an A Level Maths tutor with MyTutor

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


£20 /hr

Kamil F.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

£20 /hr

Shivani M.

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Chemistry+ 4 more

.BMAT (BioMedical Admissions)
-Medical School Preparation-

“I graduated with 5 A-levels last year and now study medicine at Exeter. I have mentored GCSE maths students for the last 2 years. I would love to hear from you!”

PremiumEllie B. GCSE Maths tutor, 11 Plus Maths tutor, A Level Maths tutor, ...
£26 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

About the author

Cosmin B.

Currently unavailable: for regular students

Degree: Computer Science (Bachelors) - University College London University

Subjects offered:Maths, Computing+ 1 more

-Personal Statements-

“I am currently a Computer Science student at University College London. I have always had a passion for science and technology  and I hope that I can share it with everyone else through my tutoring sessions. I am a calm and friendly p...”

You may also like...

Posts by Cosmin

How can we calculate the derivative of function f(x)= (x+2)/(x-1)?

How can we solve a two-equation, two-unknown values?

How can we write a C++ program to add two numbers?

The ratio between the molar mass of an alkene(A) and an alkyne(B) with the same number of carbon atoms is 1.05. Find the molecular formulas of the two hydrocarbons then write the reaction for how we can obtain the alkene A from the alkyne B.

Other A Level Maths questions

y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

What actually are sin, cos and tan?

What is differentiation and how is it done?

What are the set of values for x that satisfy the below equation?

View A Level 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