Two tanks of brine are connected via two tubes. Tank 1 contains x(t) pounds of salt in 500 gallons of brine, and tank 2 contains y(t) pounds of salt in 500 gallons of brine. Brine is pumped from tank 1 to tank 2 at a rate of 50 gallons/min and brine is pumped from tank 2 to tank 1 at the same rate of 50 gallons/min, ensuring that the total volume of brine in the tanks remains constant over time.

a) Show that x(t) and y(t) satisfy the differential equations x'= − (1/10)x + (1/10)y ; y' = (1/10)x − (1/10)y.

b) If initially tank 1 contains no salt, and tank 2 contains 10 pounds of salt, use the method of elimination to find x(t) and y(t).