Question

Find the value of k for which each of the following systems of equations have infinitely many solution:
4x+5y=3kx+15y=9

Answer 1

k = 12

Step-by-step explanation:

Given:  

4x + 5y = 3

kx + 15y = 9

The system of equations has infinitely many solutions.

a1 = 4, b1 = 5, c1 = 3

a2 = k, b2 = 15, c2 = 9

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

4/k = 1/3

Therefore k = 12

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

As, it is given equations has infinite many solutions.

We know the case of infinite many solutions.

$\Large{\star{\boxed{\rm{\frac{a_{1}} {a_{2}} = \frac{b_1}{b_2} = \frac{c_1}{c_2}}}}}$

Where,

a1 = 4, a2 = k

b1 = 5, b2 = 15

c1 = -3, c2 = -9

________________[Put Values]

$\sf{→\frac{4}{k} = \frac{5}{15} = \frac{-3}{-9}} \\ \\ \sf{→\frac{4}{k} = \frac{5}{15}} \\ \\ \sf{→k = \frac{\cancel{15} \times 4}{\cancel{5}}} \\ \\ \sf{→k = 3 \times 4} \\ \\ \sf{→k = 12} \\ \\ \Large{\star{\boxed{\sf{k = 12 }}}}$