Question

Write the set of values of a and b for which the following system of equations has infinitely many solutions.

$$\begin{gathered} 2x+3y=7 \\ 2ax+\left(a+b\right)y=28 \end{gathered}$$

Answer 1

The given equations are

For the equations to have infinite number of solutions,

Therefore

Let us take

By dividing both the sides by 7 we get,

By multiplying equations by 2 we get

Substituting from we get

Subtracting in equation we have

Hence, the value of when system of equations has infinity many solutions.