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!