RIP Brilliant Community on July 2, 2021, Question 1

$\begin{cases} x + 3y = - 2 & ...(1) \\ 3x + y = -14 & ...(2) \end{cases} \\ \begin{aligned} (1) - (2): \quad - 2x + 2y & = 12 & \small \blue{\text{Divide both sides by }2} \\ \implies y - x & = \boxed 6 \end{aligned}$

$x+3y=-2$ $\color{#D61F06}[1]$

$3x+y=-14$ $\color{#D61F06}[2]$

Solving for $x$ in $\color{#D61F06}[1]$ , we get

$x=-2-3y$

Substitute the above equation in $\color{#D61F06}[2]$ .

$3x+y=-14$

$3(-2-3y)+y=-14$

$-6-9y+y=-14$

$-8y=-8$

$y=1$

So the value of $x$ is

$x=-2-3y$

$x=-2-3(1)$

$x=-5$

Thus, the value the value of $y-x$ is

$y-x=1-(-5)=1+5=\boxed{6}$