How do I solve simultaneous equations?

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Let's use an example.



Find the values of x and y.

When I was kid back then, I was always wondering why are equations important? Well, for me, its because we want to be precise with our asnwers. 

x+y=6. There are many answers to this. Including:-



even 7+(-1)

therefore, what method should we use to ensure our calculation is accurate?

well, we have 2 equations. lets remove one variable out of the picture so we are left with only one

at the beginning, x+y=6 ......equation 1

                         2x+3y=14........equation 2

now, we decided to remove either x or y because removing either one of them will make it so much easier to find a specific value for x or y.

to do this, let's decide to remove x as an example.

multiplying equation 1 by 2 gives us,

2x+2y=12.....set this to equation 3

remember equation 2? 2x+3y=14

it can be seen now that we can remove 2x by performing equation 3-equation2 which gives us:-


we now have a value for y which is great so let's find value x by placing y=2 into equation 1, 2 or 3 since we already have a value.

let us take equation 1 in this case.


y=2, therefore, x+2=6

and x=6-2


and this, x=4 and y=2

to check our answers, we can place the values of x and y into any equations to find whether out answers match.

using equation 3,



and this is how we know our answers are correct! 

Wilson H. 11 Plus Maths tutor, 11 Plus Maths tutor

About the author

is an online GCSE Maths tutor with MyTutor studying at Bristol University

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