Consider two brine tanks connected as shown in the figure. Pure water flows into the top of tank 1 at a rate of $10 \ \mathrm{L/min}$. The brine solution is pumped from tank 1 into tank 2 at a rate of $30 \ \mathrm{L/min}$, and from tank 2 into tank 1 at a rate of $20 \ \mathrm{L/min}$. A brine solution flows out the bottom of tank 2 at a rate of $10 \ \mathrm{L/min}$. Suppose there are $40 \ \mathrm{L}$ of brine in tank 1 and $180 \ \mathrm{L}$ of brine in tank 2. Let $x$ be the amount of salt, in kilograms, in tank 1 after $t$ minutes, and $y$ the amount of salt, in kilograms, in tank 2 after $t$ minutes. Assume that each tank is mixed perfectly. Set up a system of first-order differential equations that models this situation. $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $x^{\,\prime}$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $y^{\,\prime}$ = $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $x$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $y$