Question

Find the value of k for which each of the following system of equations have infinitely many solutions :

$$\begin{gathered} 2x-3y=7 \\ \left(k+2\right)x-\left(2k+1\right)y=3\left(2k-1\right) \end{gathered}$$

Answer 1

GIVEN:

To find: To determine for what value of k the system of equation has infinitely many solutions

We know that the system of equations

For infinitely many solution

Here

Consider the following

Now consider the following

Hence for the system of equation have infinitely many solutions.