Question

Find the values of p and q for which the following system of linear equations has infinite number of solutions:

$$\begin{gathered} 2x+3y=9 \\ \left(p+q\right)x+\left(2p-q\right)y=3\left(p+q+1\right) \end{gathered}$$

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

…… (1)

Again consider

…… (2)

Multiplying eq. (2) by 3 and subtracting from eq. (1)

Putting the value of q in eq. (2)

Hence for and the system of equation has infinitely many solution.