The graph of two equations along with the points of intersection are given. Substitute the points of intersection
into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-
A)Yes
B)No

Question

The graph of two equations along with the points of intersection are given. Substitute the points of intersection
into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-
A)Yes 
B)No

Quizplus · Accepted Answer

If the points of intersection are obtained by solving the system of equations, then they should satisfy both equations. Therefore, substituting the points of intersection into the system of equations and getting a true statement confirms that the points are solutions to the system. Since the question states that the points of intersection are given along with the graph of the equations, we can assume that they are obtained by finding the intersection points of the two graphs. Substituting them into the equations and getting a true statement confirms that they are indeed solutions to the system. Points of intersection occur where the two equations are equal to each other. Therefore, when we substitute the point of intersection into each equation, we are essentially replacing both x and y with the same values. If the values satisfy both equations, then the point is a solution to the system. Since the question asks whether the points of intersection are solutions, the answer is yes.

The Graph of Two Equations Along with the Points of Intersection