1. ## Linear equations problem

Hi all, I'm working on this problem and for some reason, seem to keep getting stuck in a loop of wrong answers.

So we're given:
x + y = 1, 0.7x + 0.2y = x, and 0.3x + 0.8y = y

I'm instructed to multiply the terms by 10 to simplify, and to combine the like terms in order to solve:

___x + 2y = 0

and

___x - 2y = 0

The answer is -3 and 3, but I don't know how to arrive at that.

Any help will be much appreciated!

2. ## Re: Linear equations problem

Multiplying the 2nd equation by 10, we get,
$\displaystyle 7x + 2y = 10x$
$\displaystyle \therefore 7x-10x+2y=0$
$\displaystyle \therefore -3x+2y=0$

3. ## Re: Linear equations problem

Beautiful! Such a simple thing; I didn't see how easy this was. Yet another example of how math is a great exercise in attention to detail. Thanks!

4. ## Re: Linear equations problem

If you want a more "normalized" way of doing it, in case you can't see it like that, check this image.

5. ## Re: Linear equations problem

That's also very helpful, thanks Richard! I saw it right away with KJ's post-- my mistake was in not also multiplying the right side of the two equations (x, and y, respectively) when multiplying the left side by 10.

This is my first post on here asking for help and I am very pleased and impressed with this, thanks so much for the quick replies! I'll try to do the same where I can.