Question

Solving systems of linear equations graphically: Mastery test involves determining the intersection points of two linear equations on a graph. Which of the following statements is correct regarding these intersection points?

A) The intersection points represent the solutions to the system of equations.
B) The intersection points have no mathematical significance.
C) The intersection points always lie on the y-axis.
D) The number of intersection points is always equal to the sum of coefficients in the equations.

Answer 1

The intersection points represent the solutions to the system of equations.

Step-by-step explanation:

The correct statement regarding the intersection points of two linear equations on a graph is A) The intersection points represent the solutions to the system of equations.

When graphing two linear equations, the intersection point(s) on the graph represent the values of x and y that satisfy both equations simultaneously. These values are the solutions to the system of equations. A system of linear equations can have one solution (the lines intersect at one point), no solution (the lines are parallel and do not intersect), or infinitely many solutions (the lines are coincident and overlap).

Therefore, option A is correct.