Part 1 of 2
A player scored 102 points in a single professional basketball game. He made a total of 66 baskets, consisting of field goals (worth two points) and foul shots (worth one point). Find the number of field goals and the number of foul shots that the player made.

Step 1 ：Let's denote the number of field goals as \(x\) and the number of foul shots as \(y\).

Step 2 ：From the problem, we know two things:

Step 3 ：1. The total number of baskets is 66, so we can write this as an equation: \(x + y = 66\).

Step 4 ：2. The total number of points is 102. Since each field goal is worth two points and each foul shot is worth one point, we can write this as another equation: \(2x + y = 102\).

Step 5 ：Now we have a system of two equations:

Step 6 ：\[\begin{align*} x + y &= 66 \\ 2x + y &= 102 \end{align*}\]

Step 7 ：We can solve this system by subtracting the first equation from the second to eliminate \(y\):

Step 8 ：\[\begin{align*} 2x + y - (x + y) &= 102 - 66 \\ x &= 36 \end{align*}\]

Step 9 ：Substitute \(x = 36\) into the first equation:

Step 10 ：\[\begin{align*} 36 + y &= 66 \\ y &= 66 - 36 \\ y &= 30 \end{align*}\]

Step 11 ：So, the player made 36 field goals and 30 foul shots.

Step 12 ：To check our solution, we can substitute these values back into the original equations:

Step 13 ：\[\begin{align*} 36 + 30 &= 66 \\ 2*36 + 30 &= 102 \end{align*}\]

Step 14 ：Both equations are true, so our solution is correct.

Step 15 ：The final answer is \(\boxed{x = 36, y = 30}\)