If 2x + 3y = 14 and 2x – 3y = 2, find value of xy.

1.	If 2x + 3y = 14 and 2x – 3y = 2, find value of xy.
Answer» We know that the given equations are 2x + 3y = 14… equation (i) 2x – 3y = 2… equation (ii) Now, let us square both the equations and subtract equation (ii) from equation (i), we get, (2x + 3y)² – (2x – 3y)² = (14)2 – (2)² 4x² + 9y² + 12xy – 4x²– 9y² + 12xy = 196 – 4 24xy = 192 xy = 8 ∴ The value of xy is 8.

Answer»

We know that the given equations are

2x + 3y = 14… equation (i)

2x – 3y = 2… equation (ii)

Now, let us square both the equations and subtract equation (ii) from equation (i), we get,

(2x + 3y)² – (2x – 3y)² = (14)2 – (2)²

4x² + 9y² + 12xy – 4x²– 9y² + 12xy = 196 – 4

24xy = 192

xy = 8

∴ The value of xy is 8.

Discussion

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