At the arcade, Ryan, Sara, and Tim played video racing games, pinball and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Sara spent $12 for 3 racing games, 4 pinball games, and 5 games of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games, and 4 games of air hockey.
Write a system of three equations that represents the cost of the games that Ryan, Sara, and Tim played.

Find the cost of each game.

I also want to know how you figured this out, not just the answers