If the system of equation has infinitely many solution then 2x+3y=7 2ax+a+by=28
Answers
On comparing the given equation 2x + 3y = 7 and 2ax + a + by = 28 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 we get ,,,,
a1 = 2 , b1 = 3 , c1 = -7
a2 = 2a , b2 = b , c2 = a - 28
WKT ,,,
if the pair of equation has infinitely many solutions than
a1 / a2 = b1 / b2 = c1 / c2
=> a1 / a2 = b1 / b2
=> 2 / 2a = 3 / b
=> 2b = 6a
=> b = 3a -------- ( 1 )
=> b1 / b2 = c1 / c2
=> 3 / b = -7 / a - 28
=> 3 ( a - 28 ) = -7b
=> 3a - 84 = -7 ( 3a ) [ from eqn ( 1 ) ]
=> 3a + 21a = 84
=> 24a = 84
=> a = 7 / 2
from ( 1 )
b = 3a
b = 3 × 7 / 2
b = 21 / 2
=> 2ax + a + by = 28
=> 2 × 7/2 x + 7/2 + 21/2 y = 28
=> 7x + 21/2 y = 28 - 7/2
=> 7x + 21/2 y = 56 - 7 / 2
=> 7x + 21/2 y = 49/2
=> 14x + 21y / 2 = 49 / 2
=> 14x + 21y = 49 is the required equation .....
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