The solution to the system of equations, 300 + 30x = 200 + 35x, reveals that Jenny needs to swim 20 laps to cover the same distance at either the rec center or gym pool.
Let's use plain text to explain the system of equations and the solution:
Let "x" be the number of laps Jenny needs to swim. In the rec center pool, she covers a total distance of 300 meters for the warm-up plus 30 meters per lap, expressed as "300 + 30x". In the indoor pool, the total distance is the warm-up plus the main set, which is 200 meters plus 35 meters per lap, written as "200 + 35x".
The system of equations is:
300 + 30x = 200 + 35x
Solving for "x":
300 - 200 = 35x - 30x
100 = 5x
x = 20
Jenny needs to swim 20 laps to cover the same distance in either pool.
In a graph, the two equations 300 + 30x and 200 + 35x intersect at x = 20, indicating the point where the total distances in both pools are equal.