Question 127

The point (x, y) in the plane for which 6x + 6y = 5xy and 6y - 6x = xy is

Solution

Given, equation of planes is

6x + 6y = 5xy .......(1)

6y - 6x = xy .........(2)

Solving equation (1) + equation (2)

12y = 6xy

$$\Rightarrow$$ 12y - 6xy = 0

$$\Rightarrow$$ 6y(2-x) = 0

$$\Rightarrow$$ y = 0 or 2-x = 0

$$\Rightarrow$$ y = 0 or x = 2

From equation (1)

When y = 0, 6x + 0 = 0 $$\Rightarrow$$ x = 0

When x = 2, 6(2) + 6y = 5(2)y $$\Rightarrow$$ y = 3

$$\therefore\ $$Required point is (2,3)

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