Solving Systems of Equations

5 min

Narrative

The purpose of this Warm-up is to get students thinking about the types of questions that they might ask when looking at two lines on a graph. Based on their recent work, students may be curious about the intersection points or other points on and off the lines.

This activity uses the Co-Craft Questions math language routine to advance reading and writing as students make sense of a context and practice generating mathematical questions.

Launch

Arrange students in groups of 2. Display the graph for all to see. Use Co-Craft Questions to orient students to the context and to elicit possible mathematical questions.

Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.

Student Task

&lt;p&gt;Graph of 2 lines.&lt;/p&gt;<br>  
<p>Graph of 2 lines, origin O. Horizontal axis, scale negative 25 to 25, by 5’s. Vertical axis, scale negative 20 to 20, by 5’s. A line is labeled y equals negative x plus 10. Another line is labeled y equals 2 x plus 4. The lines intersect at the point 2 comma 8.</p>  

Sample Response

Sample responses:
  • What are the coordinates of the intersection point?
  • Give an example of a point that is on only 1 line. What does that mean for the equation associated with each line?
  • Give an example of a point that is not on either line. What does that mean for the equations?
  • Write a situation that would result in these 2 lines.

Synthesis

Invite several partners to share one question with the class, and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as “make the equation(s) true,” “solve the system,” and “points on (or off) the line.”

Standards
Addressing
  • 8.EE.8.a·Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  • 8.EE.C.8.a·Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

15 min

15 min