b. Graph all six equations on the coordinate grid and label them.
c. Circle the two equations that form a system with infinite solutions.
d. Put a square around the two equations that form a system with no solution.
e. Underline the two equations that form a system with one solution.
What do you notice about equations that are in each of these categories? Use
complete sentences to answer the questions that follow
b. Without the equations provided, I am unable to graph them or label them on the coordinate grid.
c. The two equations that form a system with infinite solutions are typically lines that are coincident or overlapping. This means that all points on one line are also on the other line.
d. The two equations that form a system with no solution are typically lines that are parallel to each other. This means that the lines never intersect and there are no common points.
e. The two equations that form a system with one solution are typically lines that intersect at a single point. This means that there is only one common point between the two lines.
The noticeability about equations in each of these categories is the relationship between the lines. For a system with infinite solutions, the lines are the same or overlapping. For a system with no solution, the lines are parallel. And for a system with one solution, the lines intersect at a single point.