Question

find the value of k if the pair of equations 2x+15y=k and kx+45y=18 has infinitely many solutions​

Answer 1

Note:

If we consider linear equations in two variables, say;

a1x + b1y + c1 = 0 and

a2x + b2y + c2 = 0

Then,

The condition for infinitely many solutions ( coincidence) is given as;

a1/a2 = b1/b2 = c1/c2

Here,

The given pair of linear equations is:

2x + 15y = k OR 2x + 15y - k = 0

And

kx + 45y = 18 OR kx + 45y - 18 = 0

Clearly, we have;

a1 = 2

a2 = k

b1 = 15

b2 = 45

c1 = - k

c2 = - 18

Thus,

The condition for infinitely many solutions ( coincidence) is given by;

=> a1/a2 = b1/b2 = c1/c2

=> 2/k = 15/45 = -k/-18

=> 2/k = 1/3 = k/18

Thus;

=> 2/k = 1/3

=> k = 2•3 = 6

OR

=> 1/3 = k/18

=> k = 18/3

=> k = 6

Hence,

The required value of k is 6.

Answer 2

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