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Popular >

x+y=2xy,x-y=xy

Solution

x + y = 2 x y, x - y = x y

Solution

(x = 2, y = \frac{2}{3} x = 0, y = 0)

Solution steps

[x + y = 2 x y x - y = x y]

Isolate

x

for

x + y = 2 x y : x = - \frac{y}{1 - 2 y}; y \neq = \frac{1}{2}

Substitute

x = - \frac{y}{1 - 2 y}

[- \frac{y}{1 - 2 y} - y = (- \frac{y}{1 - 2 y}) y]

Simplify

[\frac{- 2 y + 2 y ^{2}}{1 - 2 y} = - \frac{y ^{2}}{1 - 2 y}]

\frac{- 2 y + 2 y ^{2}}{1 - 2 y} = - \frac{y ^{2}}{1 - 2 y} : y = \frac{2}{3}, y = 0

For

y = \frac{2}{3} : x = 2

For

y = 0 : x = 0

The solutions to the system of equations are:

(x = 2, y = \frac{2}{3} x = 0, y = 0)

Popular Examples

f(x)=5,x^2= 1/2

f (x) = 5, x^{2} = \frac{1}{2}

(10)/((x+y))+2/((x-y))=4,(15)/((x+y))-5/((x-y))=-2

\frac{10}{( x + y )} + \frac{2}{( x - y )} = 4, \frac{15}{( x + y )} - \frac{5}{( x - y )} = - 2

15 a = 3, b = 5 c

u^{53} n = 3 u, m = 5

2a^2=3,b+82b^2=3a+8a^2+b^2

2 a^{2} = 3, b + 82 b^{2} = 3 a + 8 a^{2} + b^{2}

Frequently Asked Questions (FAQ)

What is x+y=2xy,x-y=xy ?
The solution to x+y=2xy,x-y=xy is