Question

russ is solving an equation where both sides are linear expressions. he sets the expressions equal to y and graphs the system finding that they are the same line. how should russ interpret this outcome?

there are no intersection points
there is exactly one intersection point
there are exactly two intersection points
there are infinitely many intersection points

Explanation:

Analyze the geometric relationship of the graphed lines

The problem states that Russ graphs the system of two linear equations and finds that "they are the same line." When two equations represent the exact same line, they are coincident.

Determine the number of intersection points

Since the two lines lie directly on top of each other, every single point on one line is also a point on the other line. A line consists of an infinite number of points. Therefore, the two lines intersect at infinitely many points.

Answer:

• There are no intersection points
• There is exactly one intersection point
• There are exactly two intersection points
• There are infinitely many intersection points (Correct answer)