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.
c. There are no equations mentioned in the text.
d. There are no equations mentioned in text.
e. There are no equations mentioned in text.
There are no equations mentioned in the text, so it is not possible to determine any patterns or characteristics of equations that fall into each category.
To determine the equations that fall into each category, let's examine the characteristics of each.
c. The equations that form a system with infinite solutions are usually two equations that represent the same line. When graphed, both lines will overlap completely, indicating that they intersect at every point and have an infinite number of solutions.
d. The equations that form a system with no solution are usually two equations that represent parallel lines. When graphed, the lines will never intersect, indicating that there is no common solution.
e. The equations that form a system with one solution are usually two equations that represent intersecting lines. When graphed, the lines will have only one point of intersection, indicating that there is only one common solution.
In summary, equations that have infinite solutions are often multiples or representations of the same line, equations that have no solution are usually parallel lines, and equations that have one solution are usually intersecting lines.