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hint: get everything to one side in `x=y`

Would I do that by dividing or adding y ?

you can think of `x=y` as `x=0+y`
the 0 added to anything doesn't change it

then try to undo that `+y`

so it turns into
x-y=0?
2x+4y=7
which turns into
[1 1] [x ] = [0]
[2 4 ] [y ] = [7]

you made an error on your matrix
but you have the correct system

-1

1 -1
2 4

so then I'd find the inverse of the coefficient matrix? and times that by the solution matrix?

what would that inverse be

[0.67 0.17]
[-0.33 0.17]

as fractions you should have
\[\Large \begin{bmatrix} 2/3 & 1/6 \\ -1/3 & 1/6\end{bmatrix}\]

and then times that by [0]
[7]
which should equal
[1.67]
[1.67]

Yeah I think I got mate. Thanks.

I don't agree with the 1.67 part

it's close though

1.16?

yes, or 1.167

you'll find that x = 7/6, y = 7/6

Thanks.

Misscalc

no problem

If it was
3x=y+1
y=x+2
Does it turn into
3x-y=1
-2=x-y

then you can flip `-2=x-y` into `x-y = -2`
but yeah, you have it correct

So if I got
-2=x-y
can you just flip it round to x-y=-2
as they are the same equations?

yeah because `a = b` is the same as `b = a` (symmetric property of equality)

y-x=2 turns into -x+y = 2
I swapped the x and y terms
you can think of the y as 0+y

exactly, the idea is that the two pair up and multiply to 1
5*(1/5) = 1
6*(1/6) = 1

you're welcome