Consider the following system of linear equations.

$$ x_1+2 x_2=b_1 ; 2 x_1+4 x_2=b_2 ; 3 x_1+7 x_2=b_3 ; 3 x_1+9 x_2=b_4 $$

Which one of the following conditions ensures that a solution exists for the above system?

For the solid $S$ shown below, the value of $\iiint_S x d x d y d z$ (rounded off to two decimal places) is $\_\_\_\_$ .

$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2 X-6$, the conditional probability $P(Y \leq 7 \mid X \geq 5)$ (rounded off to three decimal places) is $\_\_\_\_$ .

Which one of the following options contains two solutions of the differential equation $\frac{d y}{d x}=(y-1) x$ ?