what is the solution of the following system of equation? 2x-6=2y
3-2x=y

- anonymous

what is the solution of the following system of equation? 2x-6=2y
3-2x=y

- schrodinger

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- anonymous

x=2 and y=-1

- anonymous

plug in 3-2x for y for the equation 2x-6

- anonymous

right, substitute: you could do as bradley said:
y = (3 - 2x) --> (2x - 6) = 2*(3 - 2x) --> (2x-6) = (6 - 4x)

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- anonymous

so 2x + 4x -6 = 6, therefore 6x - 6 = 6, therefore x = 12/6 = 2, x = 2, now use the fact that 3-2x=y --> y now is 3-2*(2) = 3-4 = -1 --> (x,y) = ( 2, -1 )

- anonymous

ok. i am going to see if i can understand it so i can work on my next one

- anonymous

so, just tell me how i sovled it?

- anonymous

so you get the general concept

- anonymous

i am confused

- anonymous

ok, what is confusing now?

- anonymous

i guess the way it is written

- anonymous

ok, you have two equations and two variables

- anonymous

toussainr might be able to explain it differently...

- anonymous

ok, well then: the goal is find the values for each variable that satisfy both equations

- anonymous

My browser just froze, sorry

- anonymous

dpflan, please go ahead!!!

- anonymous

okay, I'm going to give it try, hoping I'm helpful

- anonymous

you have to equations. we are going to proceed in steps to make things easier!!!

- anonymous

1. You move terms in 'x' and 'y' to the left hand side (LHS) and the constants to the right hand side (RHS)

- anonymous

So we have: 2x-2y = 6

- anonymous

AND

- anonymous

-2x-y = -3

- anonymous

Let's move on with step two

- anonymous

2. From equation "-2x-y = -3"
Let's derive a value for 'y'

- anonymous

We have -y = -3+2x
OR
y = 3-2x (we multiply by -1 the LHS and the RHS)

- anonymous

This value: "y = 3-2x" we are going to replace it in the first equation : 2x-2y = 6

- anonymous

We have now:

- anonymous

2x - 2 (3-2x) = 6

- anonymous

Let's multiply,. we have:
2x - 6 + 4x = 6

- anonymous

Let's perform the required addition: 6x-6 = 6

- anonymous

let's divide by 6 the RHS and the LHS, we have now : "x - 1 = 1"

- anonymous

Form here we can easily find the value of x :" x = 2"

- anonymous

Recall that y = 3-2x
So, we replace: y = 3 - 2 * 2 ( * stands here for multiplication )
And finally y = 3 -4
y = -1

- anonymous

THAT"S THE BEST I CAN DO!

- anonymous

thank you. I understand it more now. :)

- anonymous

Okay!!!
Just to quote John Von Neuman : "You don't understand maths, you get accustomed to it"
So do a many exercises as you can! That's the key to successful mathematics!

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