Question

find the value of a for which the following pair of equation has infinitely many solution x-4y-9=0, 2x-ay-27=0​

Answer 1

For infinite many solution

a1/à2=b1/b2=c1/c2

1/2=-4/-a=-9/-27

1/2= -4/-a. -4/-a=-9/-27

a=4/2. 9a=27*4

a=2. a=27*4/9

a=2. a=12

since a=2 or 12

Answer 2

Concept

Given two linear equations a1x + b1y +c = 0 and a2x + b2y + c2 = 0

the equations have infinitely many solutions if

a1/a2 = b1/b2 = c1/c2

Given

two equations

x-4y-9=0

and 2x-ay-27=0​

Find

we need to find the value of a for which the given equations have infinitely many solutions.

Solution

We have

x-4y-9=0

here, a1 = 1, b1 = -4 and c1 = -9

similarly for 2x-ay-27=0​

a2 = 2, b2 = -a, c2 = -27

thus,

a1/a2 = 1/2

b1/b2 = -a/-4

c1/c2 = -9/-27 or 1/3

Here, we can see 1/3 is not equal to 1/2

thus, a1/a2 ≠ c1/c2

Thus, the equations can never have infinitely many solutions.

Therefore, for any value of a the equations can never have infinitely many solutions.

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