How do I solve simultaneous equations?

Let's use an example.

x+y=6

2x+3y=14

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:-

4+2

3+3

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:-

y=2

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.

x+y=6

y=2, therefore, x+2=6

and x=6-2

        =4

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,

2x+2y=12

2(4)+2(2)=8+4=12

and this is how we know our answers are correct!