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Let's define variables and write a system of equations based on the given information:

- Let \( x \) be the number of 2-point questions.
- Let \( y \) be the number of 3-point questions.

We have two key pieces of information:

1. The total number of questions is 18:
   \[
   x + y = 18
   \]

2. The total number of points is 43:
   \[
   2x + 3y = 43
   \]

### Solving the System:
#### Step 1: Solve for \( x \) in terms of \( y \)
From the first equation:
\[
x = 18 - y
\]

#### Step 2: Substitute into the second equation
\[
2(18 - y) + 3y = 43
\]

\[
36 - 2y + 3y = 43
\]

\[
36 + y = 43
\]

\[
y = 7
\]

#### Step 3: Find \( x \)
\[
x = 18 - 7 = 11
\]

### Answer:
- There are **11** two-point questions.
- There are **7** three-point questions.

Would you like a step-by-step explanation or have any questions?  

Here are five related problems you might find interesting:
1. What if the test had 20 questions and was worth 50 points? How would the system change?
2. How many total points would be on a test with 25 questions, given the same scoring scheme?
3. If there were 10 three-point questions, how many two-point questions would there be?
4. Can you solve the system graphically? What would the intersection point represent?
5. How would the system change if the two-point questions were instead worth 4 points?

### Tip:
When solving a system of equations, substitution works well when one equation is easily solved for a variable, while elimination is useful when coefficients align nicely!

Next week your math teacher is giving a unit test. The test will consist of 18 questions. Some questions are worth 2 points and some questions are worth 3 points. The test is worth 43 total points. Write and solve a system of equations to determine how many 3-point questions are on the test.

Learn how to solve a system of equations to determine the number of 3-point questions on a math test. This problem involves algebraic concepts such as linear equations and substitution, suitable for students in Grades 7-9.

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