(Solved) How do you solve a system of equations with variables in the denominator?

mgrebo

wrote...

Go to Answer

Posts: 8

Rep:

11 years ago

How do you solve a system of equations with variables in the denominator?

like 1/x + 3/y = 3/4
4/x - 2/y = 2.

Please, help me on how would you solve that equation I have no idea how to.

Read 416 times

5 Replies

Report

Replies

leezysosteezy

wrote...

11 years ago

Clear fractions by multiplying by LCD
4xy(1/x + 3/y = 3/4)... 4y+12x=3xy
xy(4/x - 2/y = 2) ... 4y-2x=2xy...-4y+2x=-2xy

Solve those with elimination to get 14x=xy therefor y=14
4(14)+12x=3x(14)
56+12x=42x
56=30x
x=56/30 reduce

Report

Answer accepted by topic starter

caitlinritz

wrote...

Posts: 3

Rep:

11 years ago

Report

Related Topics

budd20

wrote...

11 years ago

Several ways, but the easiest is to temporarily substitute dummie variables:

Let a = 1/x and let b = 1/y, then we have:

a + 3b = 3/4

4a - 2b = 2.

Multiply the first equation by -4, and then add them:

-4a - 12b = -3
4a - 2b = 2

-14 b = -1
b = 1/14

Remember that this is a subst. variable, so if b = 1/14, y =14.

I'll bet you can take it from here, okay?

Report

lew

wrote...

11 years ago

To eliminate fractions in any equation, multiply each term in the equation (on both sides) by the LCD. Your first equation would become 4y + 12x = 3xy and the 2nd equation would be 4y - 2x = 2xy.

If you line these up and subtract you get the following:

4y + 12x = 3xy
4y - 2x = 2xy
--------------------------
14x = 1xy

subtract and factor:
x(14 - y) = 0

so either x = 0 (impossible, as it would make the original equation invalid) or y = 14. If y = 14, plug in to solve for x:

4(14) - 2x = 2x(14)
56 - 2x = 28x
56 = 30x
x = 56/30

Report

_vibram_

wrote...

11 years ago

-2/y = 2-4/x = (2x-4)/x
Thus y = -2x/(2x-4)
1/x +3(2x-4)/-2x = 3/4
1/x -1.5(2x-4)/x = 3/4
(1-3x +6)/x = 3/4
(7-3x)/x = 3/4
3x = 28-12x
15x = 28
x = 28/15
You can take it from here

Report

New Topic

Home Search Q & A Board Gallery Resource Library Blog Dictionary Chat	Quick Links Start a Topic Latest Topics Unanswered Questions Courses Study Tools Browse by Textbook	Social Facebook YouTube Community Stats Who's Online Trending Staff	Help About Us Take the Tour Study Tips Posting Guidelines Terms and Policies Contact Us
Biology Forums - Study Force © 2010-2024 \| Powered by SMF \| SMF © 2015, Simple Machines \| Sitemap Biology-Forums.com is not affiliated with any publisher. Book covers, title and author names appear for reference only.