What is 2x+y=2,xyx+2y=4xy ?

The solution to 2x+y=2,xyx+2y=4xy is

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2x+y=2,xyx+2y=4xy

2 x + y = 2, x y x + 2 y = 4 x y

x = 1, x = 2 + 2, x = 2 - 2, y = 0 y = - 2 - 22 y = 22 - 2

Solution steps

[2 x + y = 2 x y x + 2 y = 4 x y]

Solve

x y x + 2 y = 4 x y : y = 0, x = 2 + 2, x = 2 - 2

For

2 x + y = 2

, subsitute

y

with

0 : x = 1

For

2 x + y = 2

, subsitute

x

with

2 + 2 : y = - 2 - 22

For

2 x + y = 2

, subsitute

x

with

2 - 2 : y = 22 - 2

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

2 x + y = 2, x y x + 2 y = 4 x y

are

x = 1, x = 2 + 2, x = 2 - 2, y = 0 y = - 2 - 22 y = 22 - 2

6 x^{2} - 40 x + 24 = 0, 6 y^{2} + 100 y - 34 = 0

x_{1} = \frac{( 5 )}{3}, x^{2} = \frac{( 5 )}{5}

2 x - y = 5, - 2 x + y = - 5

x = 7 - 3 y, x^{2} - y^{2} = 39

2 x - 3 y = 7, (a + b) x - (a + b - 3) y = 4 a + b