Let's start by solving part 5a step by step.

5a. Problem Analysis:

Angel made 20 baskets, and each basket was worth either 2 points or 3 points. The total points she scored is 48.

Let:

• $x$ be the number of 2-point baskets.
• $y$ be the number of 3-point baskets.

From the problem, we can set up the following system of equations:

1. The total number of baskets:
   $x + y = 20$
2. The total points scored:
   $2x + 3y = 48$

Step 1: Solve the system of equations

We can solve this system using substitution or elimination. Let's use substitution.

From equation 1: $x = 20 - y$

Step 2: Substitute into the second equation

Substitute $x = 20 - y$ into the second equation: $2(20 - y) + 3y = 48$

Expand and simplify: $40 - 2y + 3y = 48$ $40 + y = 48$ $y = 48 - 40$ $y = 8$

So, Angel made 8 three-point baskets.

Step 3: Find $x$

Now substitute $y = 8$ into the first equation: $x + 8 = 20$ $x = 20 - 8$ $x = 12$

So, Angel made 12 two-point baskets.

Step 4: Calculate the difference

The difference between the number of 2-point and 3-point shots is: $12 - 8 = 4$

Answer to 5a:

Angel made 4 more two-point shots than three-point shots.

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For 5b, without the graph options, I can't analyze which one matches the system. However, based on the equations:

1. $x + y = 20$
2. $2x + 3y = 48$

The graph should intersect at $(12, 8)$ because Angel made 12 two-point shots and 8 three-point shots. The correct graph will show this point as the solution.

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Do you need more details or have any questions?

Here are 5 related questions:

1. How would you solve this system of equations using the elimination method?
2. What is another way to solve the system without algebra (using trial and error)?
3. How do you graph systems of linear equations?
4. How does the number of baskets change if Angel scores 50 points?
5. What would happen if Angel made only 15 baskets instead of 20?

Tip: Always check your final answer by plugging it back into both equations to ensure it satisfies the problem!