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What is the point on the xy-plane satisfying x + 10y = 10xy and 3x - 10y = 4xy?

What is the point on the xy-plane satisfying x + 10y = 10xy and 3x - 10y = 4xy? Correct Answer (20/13, 2/7)

GIVEN:

x + 10y = 10xy and 3x - 10y = 4xy

CONCEPT:

Concept of points satisfying on xy-plane.

CALCULATION:

3x - 10y = 4xy        ----(i)

x + 10y = 10xy        ----(ii)

Multiplying equation (ii) by 3 we get,

⇒ 3x + 30y = 30xy        ----(iv)

Adding and subtracting by 10y in equation (iv)

⇒ 3x - 10y + 30y + 10y = 30xy        ----(v)

From (i) and (v)

⇒ 4xy + 40y = 30xy        ----(vi)

Dividing equation (vi) by y we get,

⇒ 4x + 40 = 30x

⇒ 26x = 40

x = 20/13

⇒ y = 2/7

∴ Required point is (20/13, 2/7)

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