Let `a,lambda,mu in R,` Consider the system of linear equations `ax+2y=lambda 3x-2y=mu` Which of the flollowing statement (s) is (are) correct?A. (a) If a = -3, then the system has infinitely many solutions for all value of `lambda and mu`.B. If `a ne -3`, then the system has a unique solution fopor all values of `lambda and mu`.C. If `lambda+u=0`, then the system has infinitely many solutions for a = -3`.D. If `lambda +mu ne 0`, then the system has no solutions for a = -3.

Let `a,lambda,mu in R,` Consider the system of linear equations `ax+2y

1.	Let `a,lambda,mu in R,` Consider the system of linear equations `ax+2y=lambda 3x-2y=mu` Which of the flollowing statement (s) is (are) correct?A. (a) If a = -3, then the system has infinitely many solutions for all value of `lambda and mu`.B. If `a ne -3`, then the system has a unique solution fopor all values of `lambda and mu`.C. If `lambda+u=0`, then the system has infinitely many solutions for a = -3`.D. If `lambda +mu ne 0`, then the system has no solutions for a = -3.
Answer» Correct Answer - A If a = -3, then the two equations in the given system represent parallel lines for `-lambda ne mu i.e., lambda+mu ne 0` and so the system has no solution. So, option (d) is correct. If a = -3 and `lambda+mu=0 i.e., -lambda=mu`, then the two lines given by the above system are coincident and hence the system has infinitely many solutions. So, option (c) is correct for all values of `lambda and mu`. If `a ne -3`, then the two lines given in the system are not parallel i.e.,they are intersecting and hence the ststem has a unique solutions. So, option (b) is correct. Clearly, option(a) incorrect.

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