Question

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

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

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

5a − 4b + 21 = 0……(1)

Again

a + b + 6 = 0…… (2)

Multiplying eq. (2) by 4 and adding eq. (1)

Putting the value of a in eq. (2)

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