Consider the system of equations $a x+b y=0$ and $c x+d y=0$ where $\quad a, b, c, d \in\{0,1\}$ Statement 1 The probability that the system of equations has a unique solution, is $3 / 8$. Statement 2 The probability that the system of equations has a solution, is 1 .

Question

Aicharya · Accepted Answer

The number of all possible deteminants of the form

Out of which only 10 determinants given by

vanish and remaining six determinants have non-zero values. Hence, the required probability $=\frac{6}{16}=\frac{3}{8}$ $\Rightarrow$ Statement 1 is correct. Statement 2 is also correct as the homogeneous equations have always a solution and Statement 2 is not a correct explanation of Statement 1.

Consider the system of equations \(a x+b y=0\) and \(c x+d y=0\) where $\quad a, b, c, d \in\{0,1\}$…

Solution