Linear Programming Problem

[ItnStln511]

I do have one other problem, if you can give me a few pointers, I'd appreciate it.. I seem to be stuck. My work is below the problem:

An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide.
The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and
the artist wants the words to all be horizontal in the final mosaic. The word tiles come in two sizes: The smaller
tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles
cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What
is the minimum cost?

Here's what I worked out so far:
4x+6y(</=)20
3x+5y(>/=)16

I attempted to solve for y by using the addition method. I multiplied the first equation by 3, and the second by -4:
12x=18y=20
-12x-20y= -34

I got -2y= -4, y=2. The problem is when I go to solve for the x-variable, I get x=2 as well. I think I'm making a mistake, I just can't find where.

 

[tkhunny]

Please start with variable definition. Many, many other things simple fall out once you have done this formally.

Also, please take a look at the example you were provided. I dare you to tell me these couple of hastily written lines comes anywhere near as organized and hopeful that a correct solution can be obtained! Really, organize and be complete. Do no try to shorten it. Write it all out so you can follow it.