Let . Consider the system of linear equations aligned ax + 2y &= 3x - 2y &= aligned…

MATHEMATICS · Single correct · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

Let a,λ,μ∈Ra, \lambda, \mu \in R . Consider the system of linear equations ax+2y=λ3x−2y=μ\begin{aligned} ax + 2y &= \lambda \\ 3x - 2y &= \mu \end{aligned} Which of the following statement(s) is (are) correct? (1) If a=−3a = -3 , then the system has infinitely many solutions for all values of λ\lambda and μ\mu (2) If a≠−3a \ne -3 , then the system has a unique solution for all values of λ\lambda and μ\mu (3) If λ+μ=0\lambda + \mu = 0 , then the system has infinitely many solutions for a=−3a = -3 (4) If λ+μ≠0\lambda + \mu \ne 0 , then the system has no solution for a=−3a = -3

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