MYTUTOR SUBJECT ANSWERS

560 views

How do I solve a simple simultaneous equation?

Simultaneous equations pop up all the time in maths, science, and engineering, so being able to solve them is really useful. Although they can look a bit daunting at first, the same general rules apply to solving all of them.

Let's look at the simplest type of simultaneous equation - two equations, with two 'unknowns' - we'll call them 'x' and 'y'.

Example

2x + y = 7 (equation 1)

3x - y = 8 (equation 2)

Now, we want to find out what the values of x and y are, just like in a normal equation. This is tricky though, because here there are two things we don't know.

We solve the problem by saying that the x and y in equation one are the same as the x and y in equation two. That way, if we can find one, we will find the other.

In the example above, the solution is straightforward. Looking at the two equations, we can notice that the y terms are opposite to each other - one positive, one negative.

What we do now is take the two equations and add them together, remembering to keep the bits on the correct side of the equals sign. We get:

2x + 3x + y - y = 7 + 8

which becomes

5x = 15

so we've got rid of the y bits! This means we can find out what x is really easily. We know that 5x = 15, so:

x = 15/5 = 3

Now that we now what x is, we can find out what y is just by looking back at one of our first equations (it doesn't matter which one). Looking at equation 1:

2x + y = 7 

Because we know that x = 3, we can say that 

6 + y = 7 

and so 

y = 7 - 6

y = 1

so we've found our two unknowns, x = 3 and y = 1! We can check these by putting them back into the equations and making sure we get the right answer.

It's not always as simple as this though. We were lucky because in our example, the equations 'matched' - one had a '+ y' bit, the other one had a '- y' bit, so we could just add them to get rid of the y parts.

Often, the equations don't fit so well, and so we have to do things to them before we can use them - we can multiply, divide and rearrange equations to make them fit.

But, once they fit, we can use the same method we just used in the example to solve them!

Joe M. GCSE Maths tutor

1 year ago

Answered by Joe, a GCSE Maths tutor with MyTutor


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

560 SUBJECT SPECIALISTS

£20 /hr

Akhil P.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 6 more

Maths
Physics
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“First Year Medical student at Imperial College. Studies all 3 sciences and Maths at A-levels and did an EPQ(4 A*s and an A)”

£20 /hr

Jay G.

Degree: Biological Sciences (Biochemistry) (Bachelors) - Edinburgh University

Subjects offered:Maths, Mandarin+ 2 more

Maths
Mandarin
Chemistry
Biology

“I am here not only to help you get better at exams, but to help you enjoy your subject more”

Maya B. GCSE Maths tutor, A Level Maths tutor, 13 Plus  Maths tutor, ...
£18 /hr

Maya B.

Degree: Mathematics with Physics (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
.STEP.

“My approach is centred on deep understanding, and I constantly engage and encourage students to build both confidence and enthusiasm!”

About the author

£18 /hr

Joe M.

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered:Maths

Maths

“About Me I am a recent Aeronautical Engineering Masters-level graduate from the University of Bristol. Throughout my studies I have covered a wide range of topics, and so am familiar with what works and doesn't work when learning new ...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How do you substitute a number into an algebraic expression?

Expand and simplify (2x-5)(3x+4)

Rationalise the denominator of the fraction 3/sqrt(5)

Solve: 3(x - 2) = 21

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

mtw:mercury1:status:ok