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

Question 223603: If 3x-5y/7x-4y = 3/4, find the value of .
Many thanks!
Answer by jsmallt9(3758) (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 :

Now we just solve for . (If you have trouble following the steps below, try using a temporary variable. Let . Then replace with q: . And solve this for q. At the end, replace the q with )
Since this is a proportion, we'll start by cross multiplying:

Subtract from each side:

Add 12 to both sides:

Divide both sides by 9:

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