Question

solve (a+c)x - (a-c)y =2ab and (a-b)y =2ab by cross multiplication mathod
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Answer 1

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Answer 2

Answer: x = b and y= -b${\boxed{\green{\checkmark{}}}}$

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$\large\underline{\red{\sf \orange{\bigstar} .}}$Given$\large\underline{\red{\sf \blue{\bigstar} .}}$

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• The given equations are :(a+c)x − (a−c)y = 2ab ....(1)

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• (a+b)x − (a−b)y = 2ab ..(2)

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$\large\underline{\red{\sf \blue{\bigstar} .}}$To Find$\large\underline{\red{\sf \orange{\bigstar} .}}$

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• value of (a+c)x - (a-c)y =2ab and (a-b)y =2ab

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$\large\underline{\red{\sf \pink{\bigstar} .}}$Solution$\large\underline{\red{\sf \green{\bigstar} .}}$

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• Adding (1) and (2), we get,

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• (a+c+a+b)x − (a−c+a−b)y =4ab

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• ⇒(2a+b+c)x − (2a−b−c)y =4ab

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• ⇒(2a+b+c)x + (b+c−2a)y = 4ab ...(3)

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Subtracting (2) from (1), we get

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• (c−b)x + (c−b)y = 0

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• ⇒(c−b)(x+y) = 0

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• ⇒x + y = 0

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⇒y = − x ...(4)

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putting the value of y in (3), we get

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• (2a+b+c)x + (b+c−2a)(−x) =4ab

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• ⇒[(2a+b+c) −(b+c−2a)]x =4ab

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• ⇒(2a+b+c−b−c+2a)x = 4ab

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• ⇒4ax = 4ab

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⇒x = b⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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$\large\underline{\red{\sf \pink{\bigstar} .}}$So , y = -x = - b

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$\large\underline{\red{\sf \purple{\bigstar} .}}$Here x= b and y= - b

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