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Question

# Solve the linear equations by cross multiplication method : (a+b)x+(aâˆ’b)y=3aâˆ’b(2a2+b2)xâˆ’(a2âˆ’b)y=b2+2b

A

x=1 and y=3
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B

x=2 and y= 3
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C

x=1 and y= 2
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D

x=1 and y= 4
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Solution

## The correct option is C x=1 and y= 2 (a+b)x+(a−b)y=3a−b(2a2+b2)x−(a2−b)y=b2+2b By cross multiplication method : x(a−b)(b2+2b)−(3a−b)(−a2+b)=y(3a−b)(2a2+b2)−(b2+2b)(a+b)=−1−(a+b)(a2−b)−(2a2+b2)(a−b)x3a3−b3+ab2−a2b−b2−ab=y6a2−2b3+2ab2−2ab2−2a2b−2b2−2ab=−1−(3a3−b3+ab2−a2b−b2−ab)⇒x(3a3−b3+ab2−a2b−b2−ab)=−1−(3a3−b3+ab2−a2b−b2−ab)⇒y2(3a3−b3+ab2−a2b−b2−ab)=−1−(3a3−b3+ab2−a2b−b2−ab)⇒x=y2=1⇒x=1,y=2 So, option c is correct.

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