By comparing the ratios a1/a2, b1/b2 and c1/c2, find out for what value (s) of α, the lines
representing the following equ

1 thought on “By comparing the ratios a1/a2, b1/b2 and c1/c2, find out for what value (s) of α, the lines <br /> representing the following equ”

1. Answer:

   SOLUTION :

   Given :

   a) 5x- 4y + 8 = 0 & 7x+ 6y – 9 = 0

   b) 9x + 3y + 12 = 0 & 18x + 6y + 24 = 0

   c) 6x – 3y + 10 = 0 & 2x – y + 9 = 0

   (a)

   On comparing with a1x + b1y +c1 = 0 & a2x + b2y + c2 = 0

   a1= 5 , b1= – 4 , c1= 8

   a2= 7, b2= 6 , c2 = -9

   Now,

   a1/a2 = 5/7 , b1/b2 = – 4/6, c1/c2= 8/-9

   Since, a1/a2 ≠ b1/b2

   Hence, the lines representing the pair of linear equations are INTERSECTING at a point and have exactly one solution.

   (b) 9x + 3y + 12 = 0 & 18x + 6y + 24 = 0

   On comparing with a1x + b1y +c1 = 0 & a2x + b2y + c2 = 0

   a1= 9 , b1= 3, c1= 12

   a2= 18, b2= 6 , c2 = 24

   Now,

   a1/a2 = 9/18= 1/2 , b1/b2 = 3/6= 1/2 , c1/c2= 12/24= 1/2

   Since, a1/a2 = b1/b2=c1/c2

   Hence, the lines representing the pair of linear equations are COINCIDENT LINES and have infinitely many solutions.

   c) 6x – 3y + 10 = 0 & 2x – y + 9 = 0

   On comparing with a1x + b1y +c1 = 0 & a2x + b2y + c2 = 0

   a1= 6 , b1= -3, c1= 10

   a2=2, b2= -1, c2 = 9

   Now,

   a1/a2 = 6/2 , b1/b2 = -3/-1= 3, c1/c2= 10/9

   Since, a1/a2 = b1/b2 ≠ c1/c2

   Hence, the lines representing the pair of linear equations are PARALLEL LINES and have no many solution.

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