Let $a, λ, μ ∈ R$. Consider the system of linear equations
$ax + 2y = λ$
$3x-2y=μ$
Which of the following statement(s) is (are) incorrect?
Answer & explanation
Correct answer: option 1
If $a=-3$, then the two equations in the given system represent parallel lines for $-λ≠u$ i.e. $λ+μ ≠ 0$ and so the system has no solution. So, option (4) is correct.
If $a=-3$ and $λ+μ=0$ i.e. $-λ=μ$, then the two lines given by the above system are coincident and hence the system has infinitely many solutions. So, option (3) is correct for all values of λ and μ.
If $a≠ -3$, then the two lines given in the system are not parallel i.e. they are intersecting and hence the system has a unique solution. So, option (2) is correct.
Clearly, option (1) is incorrect.