A basketball team played 51 games. They won 19 more than they lost. How many games did they win? How many games did they lose?

Step 1 ：Let's denote the number of games the basketball team won as W and the number of games they lost as L.

Step 2 ：We know that the total number of games played is 51, so we can write this as an equation: \(W + L = 51\).

Step 3 ：We also know that the team won 19 more games than they lost, which gives us another equation: \(W = L + 19\).

Step 4 ：We can solve these two equations to find the values of W and L.

Step 5 ：The solution to the equations is \(L = 16\) and \(W = 35\).

Step 6 ：Final Answer: The team won \(\boxed{35}\) games and lost \(\boxed{16}\) games.