A strange type of simultaneous equation: ax = 64x - 64y, ay

[JJK]

Hi there. I'm not too sure where to post this question, so please forgive me if it is in the wrong place!

I am trying to invert two equations but my brain doesn't seem to be working too good today.

Given that:

ax = 64x - 64y

and

ay = 32x + 32y

How can I work out x and y if I have ax and ay?

I'm sorry if this is a no-brainer and I know I'll just kick myself when I see the answer. Thanks in advance!

 

[stapel]

I don't know what you've tried so far. This is how I would start:

You have:

. . . . .ax = 64x - 64y
. . . . .ay = 32x + 32y

Solving the first equation for "x=" gives:

. . . . .64y = 64x - ax
. . . . .64y = x(64 - a)
. . . . .(64y) / (64 - a) = x

Plugging this into the second equation gives:

. . . . .ay = 32[(64y) / (64 - a)] + 32y
. . . . .ay = (2048y) / (64 - a) + 32y
. . . . .64ay - a²y = 2048y + 2048y - 32ay
. . . . .0 = a²y - 96ay + 4096y

This is a quadratic in "a", which can be solved for "a" in terms of "y".

See where this leads.

(Note: With two equations in three unknowns, it is unlikely that you will be able to solve for numerical values of x and y.)

Eliz.

 

[JJK]

I'm terribly sorry, but this forms part of a programming task and ax is actually a variable name rather than a composite. Appologies, let me restate:

c = 64x - 64y
d = 32x + 32y

So I need to find x and y given c and d.

Thanks.

 

[Mrspi]

I'm terribly sorry, but this forms part of a programming task and ax is actually a variable name rather than a composite. Appologies, let me restate:

c = 64x - 64y
d = 32x + 32y

So I need to find x and y given c and d.

Thanks.

Multiply the second equation by 2:

c = 64x - 64y
2d = 64x + 64y

c + 2d = 128x

Divide both sides by 128:

(c + 2d) / 128 = x

Ok...now you have the value of x in terms of c and d. To find y, substitute (c + 2d) / 128 for "x" in one of the original equations.

I hope this helps you.