4. Steph Curry scored 35 points in a single game by scoring only 2-pointers and 3-pointers (no freethrows). He made a total of 12 baskets. How many 2-pointers did he make and how many 3-pointers did he make? Solve by setting up and solving a system of equations. Let $x=$ Number of 2 -point baskets made. Let $y=$ Number of 3 -point baskets made. Write an equation using the fact that he scored 33 points in the game. Write an equation using the fact that he made a total of 14 baskets in the game. Solve the system of equations.
Solution
Step 1 ：Let \(x\) be the number of 2-point baskets made and \(y\) be the number of 3-point baskets made.
Step 2 ：Write an equation using the fact that he scored 35 points in the game: \(2x + 3y = 35\).
Step 3 ：Write an equation using the fact that he made a total of 12 baskets in the game: \(x + y = 12\).
Step 4 ：Solve the second equation for \(x\), which gives \(x = 12 - y\).
Step 5 ：Substitute \(x = 12 - y\) into the first equation and solve for \(y\).
Step 6 ：This gives the equation \(2(12 - y) + 3y = 35\), which simplifies to \(24 - 2y + 3y = 35\), and further simplifies to \(y + 24 = 35\).
Step 7 ：Solving for \(y\) gives \(y = 11\).
Step 8 ：Substitute \(y = 11\) back into the equation \(x = 12 - y\) to find the value of \(x\).
Step 9 ：This gives \(x = 12 - 11 = 1\).
Step 10 ：Final Answer: Steph Curry made \(\boxed{1}\) 2-pointer and \(\boxed{11}\) 3-pointers.
