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))

B

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

C

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

D

None of these

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 + (b2c1– b1c2) = 0 i.e., (b2a1 – b1a2) x = b1c2 – b2c1 Therefore x= (b1c2−b2c1)(a1b2−a2b1), Substitute this x in any of the given equation we get  y= (c1a2−c2a1)(a1b2−a2b1) Mathematics

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