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Title: How do you solve a system of equations with variables in the denominator? Post by: mgrebo on Jun 18, 2013 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. Title: How do you solve a system of equations with variables in the denominator? Post by: leezysosteezy on Jun 18, 2013 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 Title: How do you solve a system of equations with variables in the denominator? Post by: caitlinritz on Jun 18, 2013 Content hidden
Title: How do you solve a system of equations with variables in the denominator? Post by: budd20 on Jun 18, 2013 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? Title: How do you solve a system of equations with variables in the denominator? Post by: lew on Jun 18, 2013 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 Title: How do you solve a system of equations with variables in the denominator? Post by: _vibram_ on Jun 18, 2013 -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 |