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Question

The solution (x,y) for the given pair of linear equations is a1x + b1y + c1=0 and a2x + b2y + c2=0 



A

((b1c2-b2c1)/(a1b2-a2b1), (c1a2-c2a1)/(a1b2-a2b1))

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B

((b2c2-b1c1)/(a1b2-a2b1), (c2a2-c1a1)/(a1b2-a2b1))

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C

((b2c1-b1c2)/(a1b2-a2b1), (c1a1-c2a2)/(a1b2-a2b1))

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D

None of these

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Solution

The correct option is B

((b1c2-b2c1)/(a1b2-a2b1), (c1a2-c2a1)/(a1b2-a2b1))


Let us use elimination method to solve the given pair of equations

Given two equations are a1x + b1y + c1 = 0

                                     and a2x + b2y + c2 = 0

Multiply first equation by b2 and second equation by b1, to get

b2a1x + b2b1y + b2c1 = 0

b1a2x + b1b2y + b1c2 = 0

Subtracting these two equations

(b2a1 – b1a2) x + (b2b1 – b1b2) y + (b2c1b1c2) = 0

i.e., (b2a1 – b1a2) x = b1c2 – b2c1

Therefore x= (b1c2b2c1)(a1b2a2b1),

Substitute this x in any of the given equation we get

 y= (c1a2c2a1)(a1b2a2b1)


Mathematics

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