Let `alpha, lambda , mu in R`.Consider the system of linear equations
`alphax+2y=lambda`
`3x-2y=mu`
Which of the following statement(s) is (are) correct ?

Options

A. If `a=-3` then the system has infinitely many solution for all values of `lambda` and `mu`
B. If `a=-3` then the system has a unique solution for all values of `lambda` and `mu`
C. If `lambda+mu=0`, then the system has infinitely many solution for `a=-3`
D. If `lambda+mu ne 0`, then the system has no solution for `a=-3`

Explanation

Here, `ax+2y=lambda`
and `3x-2y=mu`
For `a=-3`, above equations will be parallel or coincident, i.e. parallel for `lambda+mu ne 0` and coincident if `lambda+mu=0` nd if `a ne -3`, equations are intersecting, i.e. unique solution.