Activities

1. What is a solution to a system of linear equations?
2. Identify if the point (5, 1) is a solution to the following system of equations:

3. Jose’s homework question asked him to verify if (1, 2) was a solution to the system of linear equations y = x – 1 and y = -x + 3.  Based on his work shown below, he concluded it was the solution.  Do you agree?  Why or why not?

4. Given the graphs below of y = x and y = 2x + 1:

1. Identify the solution to the system of equations
2. Verify your answer

5. Bianca has two plants she keeps in her house that grow at different rates.  She graphed their growth, y, in inches over several months, x, as shown below.  Identify the point of intersection and explain what it means.

Answer Key/Rubric

1. The solution to a system of linear equations is an ordered pair that makes both equations true.

2. No

3. Jose is incorrect.
   Acceptable reasons may include, but are not limited to:

• Jose checked the point (2, 1) not (1, 2)
• Jose substituted into the wrong variables
• Every point is given in the form (x, y)

4. Answers as follows:
   
   
   1. (-1, -1)
   2. Check:

5. Acceptable answers may include, but are not limited to:

• Intersection: (4, 10)
• The intersection (4, 10) means that after 4 months both plants are the same height of 10 inches.