Question

Write the value of k for which the system of equations

2x – y = 5

6x + ky = 15

has infinitely many solutions.

Answer 1

Given: 2x – y = 5, 6x + ky = 15

For infinitely many solutions the two equations must be scalar multiples,

i.e. `a_1/a_2 = b_1/b_2 = c_1/c_2` 

Multiply the first equation by 3:

3(2x – y) = 3(5)

⇒ 6x – 3y = 15 

Compare with 6x + ky = 15: the y-coefficients must match, so k = –3.