Calculating Needed Alloy Using Linear System Of Equations I'm having troubles with this question which involves a linear system of equations. I keep encountering $x$ to be a negative number, which cannot be possible because you can't have a negative number of a physical item (ie: you can't have $-6$ school buses, $-2$ pencils, etc). Can someone help me figure this one out?
An artist was commisioned to make a 500 gram statue composed of 60% tin. She has 70% tin alloy and 30% tin alloy available.

1. What mass of each alloy is required to produced the desired ally? Use an elimination method to solve this problem.

This is the equations I tried:
$x + y = 500 \\
0.70x + 0.30y = 0.60$
This is what I got to eliminate $y$:
$
(x+y=500)*3 = 3x+3y = 1500 \\
(0.70x + 0.30y = 0.60)*10 = 7x+3y=6
$
Here's how I did it:
$\require{cancel}
\space\space\space\space\space\space\space\space\space3x+\bcancel{3y}\space\space\space=1500\\
- (-7x-(\bcancel{3y})=-6)\\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
x = -4x \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space= 1494\\
x = \frac{-4x}{-4} = \frac{1494}{-4} \\
x = \frac{1494}{-4} = -373.5
$
And since $x = -373.5$ then 
$y = 500 - x \\\space\space= 500 - (-373.5) \\\space\space= 873.5$
If you do it backwards then it works but (like I said), I can't see how $x$ can be a negative number. Any ideas?

I haven't worked out the problem, so I don't know if this will solve all your issues, but it seems to me that your system of equations might be incorrect. Take a look at your second equation:
0.70x + 0.30y = 0.60
Now, from your first equation, we can assume that x is the necessary number of grams of alloy 1 and y is the necessary number of grams of alloy 2. Following this logic, your second equation is dealing with concentrations. Now, 0.70x + 0.30y should give you the amount of total tin being used. If that's correct, this expression should equal the desired amount of tin in the finished product (i.e. 0.60*500g). Ergo, your second equation should be 0.70x + 0.30y = 300.  Hopefully this helps.
