Question

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

$$\begin{gathered} 2x+3y=7 \\ \left(k+1\right)x+\left(2k-1\right)y=4k+1 \end{gathered}$$

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

Now again consider the following to find k

Hence for the system of equation have infinitely many solutions