An Algebra I test contains 30 questions. Some of the questions are worth 4 points each, and some are worth 2 points each. The total test is worth 100 points. Let f represent the number of questions worth 4 points and t, the number of questions worth 2 points.

Solve the system by elimination to find how many two-point questions the test contains

f + t = 30

4f + 2t = 100

4f + 4t = 120
4f + 2t = 100

2t = 20
t = 10
So, f = 20

To solve the system of equations, we need to set up the equations based on the given information.

Let f represent the number of questions worth 4 points and t represent the number of questions worth 2 points.

From the given information, we know that the total number of questions is 30. This can be represented as the equation:

f + t = 30 --------(1)

We also know that the total points for the test is 100. Since each 4-point question contributes 4 points and each 2-point question contributes 2 points, we can set up the equation:

4f + 2t = 100 --------(2)

Now, we need to solve these two equations using elimination:

Multiply equation (1) by 2 to eliminate t:

2f + 2t = 60 --------(3)

Subtract equation (3) from equation (2) to eliminate t:

(4f + 2t) - (2f + 2t) = 100 - 60

2f = 40

Divide both sides by 2:

f = 20

So, there are 20 questions worth 4 points.

Substitute this value of f into equation (1) to solve for t:

20 + t = 30

Subtract 20 from both sides:

t = 10

Therefore, there are 10 questions worth 2 points on the test.