There are two alloys, one is 1 part silver and 5 parts copper and the other 3 parts silver and 1 part copper are mixed to form 350 pounds of an alloy that is equal in silver and copper content. how many pounds of each should be used?

Lets make x equal the number times you use the 1/5 ratio alloy and y equal the number of times you use the 3/1 ratio alloy.  You can make the equation (x+3y)-(5x+y)=0 and (x+3y)+(5x+y)=350
Then you can make the system of equation of:
-4x+2y=0 (this is y=2x)
 6x+4y=350  
You can make 6x+8x=350 by through substitution and solve of x.
14x=350
x=25 (which means y=50)

that means that the weight of the 1/5 ratio alloy is 150 pounds.
(25+(5x25))=150
the weight of the 3/1 ratio alloy is 200 pounds.
((50x3)+50)=200

I hope this helps.