SOLUTION: If 3x-5y/7x-4y = 3/4, find the value of {{{ x/y }}}. Many thanks!

Algebra ->  Equations -> SOLUTION: If 3x-5y/7x-4y = 3/4, find the value of {{{ x/y }}}. Many thanks!      Log On


   



Question 223603: If 3x-5y/7x-4y = 3/4, find the value of +x%2Fy+.
Many thanks!

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this problem is to notice that you are not asked to find x and/or y. This would not be possible because you generally need two equations (or more) to solve for the values of two variables.

You are only asked to find x/y, which we can find without finding x or y! All we have to do is transform the equation so it is expressed in terms of x/y (without any solitary x's or y's. With your equation this is fairly simple. Just multiply the numerator and denominator of the left side by 1%2Fy:
%283x-5y%29%2F%287x-4y%29+=+3%2F4
%28%283x-5y%29%2F%287x-4y%29%29%28%281%2Fy%29%2F%281%2Fy%29%29+=+3%2F4
%283%28x%2Fy%29-5%29%2F%287%28x%2Fy%29-4%29+=+3%2F4
Now we just solve for x%2Fy. (If you have trouble following the steps below, try using a temporary variable. Let q+=+x%2Fy. Then replace x%2Fy with q: %283q-5%29%2F%287q-4%29+=+3%2F4. And solve this for q. At the end, replace the q with x%2Fy)
Since this is a proportion, we'll start by cross multiplying:
%283%28x%2Fy%29-5%29%284%29+=+%287%28x%2Fy%29-4%29%283%29
12%28x%2Fy%29-20+=+21%28x%2Fy%29-12
Subtract 12%28x%2Fy%29 from each side:
-20+=+9%28x%2Fy%29-12
Add 12 to both sides:
-8+=+9%28x%2Fy%29
Divide both sides by 9:
%28-8%29%2F9+=+x%2Fy