standard_description: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
problem_activity: Task
The 54 students in one of several middle school classrooms were asked two questions about musical preferences: “Do you like rock?” “Do you like rap?” The responses are summarized in the table below.
|     Likes Rap     | Doesn't Like Rap | Row Totals |
|-------------------|------------------|------------|
|    Likes Rock     |                  |            |
| Doesn't Like Rock |                  |            |
|   Column Totals   |                  |            |
Is this a random sample, one that fairly represents the opinions of all students in the middle school?
What percentage of the students in the classroom like rock?
Is there evidence in this sample of a positive association in this class between liking rock and liking rap? Justify your answer by pointing out a feature of the table that supports it.
Explain why the results for this classroom might not generalize to the entire middle school.


aligns: no