SOLUTION: Solve for x and y: 2/x + 1/y = 4/5 3/x =5/y = 19/6

Question 713462: Solve for x and y:
2/x + 1/y = 4/5
3/x =5/y = 19/6
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
(2)/(x)+(1)/(y)=(4)/(5)
Move all terms not containing x to the right-hand side of the equation.
(2)/(x)=(4y-5)/(5y)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
2*5y=(4y-5)*x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(4y-5)*x=2*5y
Multiply (4y-5) by x to get x(4y-5).
x(4y-5)=2*5y
Multiply 2 by 5y to get 10y.
x(4y-5)=10y
Multiply x by each term inside the parentheses.
4xy-5x=10y
Factor out the GCF of x from 4xy-5x.
x(4y-5)=10y
Divide each term in the equation by (4y-5).
-->Solution x=(10y)/(4y-5)
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(2)/(x)+(1)/(y)=(4)/(5)
Move all terms not containing y to the right-hand side of the equation.
(1)/(y)=(2(2x-5))/(5x)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
1*5x=2(2x-5)*y
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
2(2x-5)*y=1*5x
Multiply 2 by y to get 2y.
2y(2x-5)=1*5x
Multiply 1 by 5x to get 5x.
2y(2x-5)=5x
Multiply 2y by each term inside the parentheses.
4xy-10y=5x
Factor out the GCF of 2y from 4xy-10y.
2y(2x-5)=5x
Divide each term in the equation by (2x-5).
2y=(5x)/(2x-5)
Divide each term in the equation by 2.
-->Solution y=(5x)/(2(2x-5))
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(3)/(x)=(5)/(y)=(19)/(6)
This equation cannot be solved algebraically.
No Algebraic Solution

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