Question 1119862

Need another question validated please.

Bill and Mary are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Bill sold 4 rolls of plain wrapping paper and 2 rolls of holiday wrapping paper for a total of $86. Mary sold 12 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for a total of $243. What is the cost each
of one roll of plain wrapping paper and one roll of holiday wrapping paper?

What I did to solve:

Let x= represent price of plain wrapping paper
Let y= represent price of holiday wrapping paper

4x + 2y = 86
12x + 5y = 243

3(4x + 2y) = 3(86)
-1(12x + 5y) = -1(243)

12x + 6y = 258
-12x - 5y = 243
---------------
       1y = 15

4x + 2(15) = 86
4x + 30 = 86
4x + 30 - 30 = 86 - 30
          4x = 56

          4x = 56
          --   --
          4     4

          x  = 14

The part that is throwing me of is 1y = 15. It doesn't seem right.

Thanks for your time.
<pre>You did everything correctly, and 1y = 15 is the same as y = 15. The coefficient on all variables without a noticeable coefficient is 1, OR,
you can just easily DIVIDE each side by 1, as follows: {{{matrix(1,5, y, "=", 15/1, "=", 15)}}}, but that's taking it to the extreme because ANYTHING divided by 1 is ITSELF.