As stated previously, this content standard is in 8^th grade Expressions and Equations. This content standard can be adapted in various ways depending on the level of understanding present in the mathematics classroom. Teachers can begin with simple linear equations like x + y=9, and once the level of understanding increases, the complexity of the linear equations may increase, 2.5x = 20y + 5.

Examples relating to part c may or may not have points of intersection. It would be interesting to see how students determine when two lines do not intersect. Desmos may be implemented in the classroom when covering this standard because it allows students to explore various systems of linear equations. For an added challenge, students may work with Desmos to see what occurs when multiple equations are in a system.

For example:

This example shows that a third linear equation has the same point of intersection with the other two liner equations. Thus, the point (2,7) satisfies all three linear equations simultaneously.

Let’s wrap this up on the conclusions page!