Question

Prove that there is a value of c(≠ 0) for which the system has infinitely many solutions. Find this value.

6x + 3y = c − 3
12x + cy = c

Answer 1

GIVEN:

To find: To determine for what value of c the system of equation has infinitely many solution

We know that the system of equations

For infinitely many solution

Here

Consider the following

Now consider the following for c

But it is given that c ≠ 0. Hence c = 6

Hence for the system of equation have infinitely many solutions.