**At a basketball  game, a team made 56 successful shots. They were a combination of  1- and  2 point shots. The team scored 92 points in all. Write and solve a system of equations to find  the number of each type of shot.**

There were 36,   2-point shots and 20, 1-point shots.

There were 25,  2-point shots and 15, 1-point shots.

There were 10, 2-point shots and 14, 1 -point shots.

There were 15,  2-point shots and 12, 1-point shots.

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To solve this problem, we need to write a system of equations based on the information given:

### Variables:
- Let \( x \) be the number of 1-point shots.
- Let \( y \) be the number of 2-point shots.

### Equations:
1. The total number of shots is 56:
   \[
   x + y = 56
   \]
2. The total points scored is 92:
   \[
   x + 2y = 92
   \]

Now, we solve this system of equations.

---

### Step 1: Solve for \( x \) in terms of \( y \) from the first equation:
\[
x = 56 - y
\]

---

### Step 2: Substitute \( x = 56 - y \) into the second equation:
\[
(56 - y) + 2y = 92
\]
Simplify:
\[
56 + y = 92
\]
\[
y = 92 - 56
\]
\[
y = 36
\]

---

### Step 3: Substitute \( y = 36 \) back into \( x = 56 - y \):
\[
x = 56 - 36
\]
\[
x = 20
\]

---

### Final Solution:
- \( x = 20 \): The team made 20 one-point shots.
- \( y = 36 \): The team made 36 two-point shots.

### Verification:
- Total shots: \( 20 + 36 = 56 \) (Correct)
- Total points: \( 20(1) + 36(2) = 92 \) (Correct)

Thus, the solution matches the problem.

---

Let me know if you'd like further clarification or details!

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### Related Questions:
1. How do you represent a system of equations graphically for this problem?
2. How can substitution and elimination methods be compared for solving this system?
3. What would change if the total points were 100 instead of 92?
4. How can this problem be adapted for a scenario with 3-point shots included?
5. What is the significance of ensuring solutions satisfy all equations in the system?

### Tip:
Always double-check your solution by substituting it back into the original equations to verify accuracy.

At a basketball game, a team made 56 successful shots. They were a combination of 1- and 2-point shots. The team scored 92 points in all. Write and solve a system of equations to find the number of each type of shot.

Learn how to solve a system of equations involving basketball shots. This problem explores algebraic methods, including substitution and elimination, to determine the number of 1-point and 2-point shots. Suitable for Grades 7-9 students.

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