We can solve this problem using a system of linear equations.

Let:

• $x$ represent the number of 2-pointers Jack made.
• $y$ represent the number of 3-pointers Jack made.

From the information in the problem, we can set up two equations:

1. The total number of shots Jack took is 12: $x + y = 12$

2. The total points Jack scored is 30. Each 2-pointer gives 2 points, and each 3-pointer gives 3 points: $2x + 3y = 30$

Solving the system of equations:

Step 1: Solve the first equation for $x$: $x = 12 - y$

Step 2: Substitute $x = 12 - y$ into the second equation: $2(12 - y) + 3y = 30$ $24 - 2y + 3y = 30$ $24 + y = 30$ $y = 30 - 24 = 6$

Step 3: Substitute $y = 6$ into the first equation to find $x$: $x + 6 = 12$ $x = 12 - 6 = 6$

Conclusion:

Jack made 6 two-pointers and 6 three-pointers.

---

Would you like more details on how to solve this, or do you have another question? Here are some related questions:

1. How can you solve a system of equations using substitution?
2. What happens if the total points scored is different (for example, 28)?
3. What other real-life scenarios can be modeled with systems of linear equations?
4. How can you check if your solution is correct?
5. How would the solution change if Jack had only taken 10 shots?

Tip: If you're ever unsure of your steps, you can always check the solution by substituting your values back into the original equations.