Let's define the variables for the problem:

• Let $x$ represent the number of two-point shots Isaiah made.
• Let $y$ represent the number of free throws Isaiah made.

Setting up the Equations

1. Total Points Equation: Since each two-point shot is worth 2 points, and each free throw is worth 1 point, we know that the total points scored is 12. So we can write: $2x + y = 12$

2. Relationship Between Free Throws and Two-Point Shots: Isaiah made 4 times as many free throws as two-point shots. This gives us: $y = 4x$

System of Equations

The system of equations is:

2x + y = 12 \\ y = 4x \end{cases}$$ This system can now be solved to find the values of $$x$$ and $$y$$, representing the number of two-point shots and free throws, respectively. Would you like me to solve this system as well? --- Here are some additional questions related to this setup: 1. How would the system change if Isaiah scored a different total, like 15 points? 2. What if Isaiah made 3 times as many free throws as two-point shots instead? 3. How could we set up a system if there were three types of scoring (free throws, two-point shots, and three-point shots)? 4. If Isaiah scored all 12 points from only free throws, how would the system of equations change? 5. How could you verify the solution to the system? **Tip:** When setting up systems of equations, clearly define each variable to avoid confusion about what each term represents.