Question

For what value of k will the following linear system have infinitely many solutions?

2a+b=-6, 6a+kb=-18

Answer 1

There are infinitely many solutions to a linear equation with the same variable term on both sides of the equation.

We have to find the coefficient of "b"

from first equation:

• 2a + b = -6

• b = -6 - 2a

from second equation:

• 6a + kb = -18

• b = (-18 - 6a)/k

solve them simultaneously:

• (-18 - 6a)/k = -6 - 2a

• (-18 - 6a)/(-6 - 2a) = k

• k = 3