Question

Which statement is true for any linear system of two equations in two variables?

A) The system is independent if the slopes of the two lines are equal.
B) The system is inconsistent if the y-intercepts of the two lines are equal.
C) The system is independent if the graphs of the two equations intersect once.
D) The system is dependent if it has no real solution.
E) The system is always consistent if the slopes of the two lines are equal.

Answer 1

The correct statement for any linear system of two equations in two variables is C) The system is independent if the graphs of the two equations intersect once.

Step-by-step explanation:

The correct statement for any linear system of two equations in two variables is C) The system is independent if the graphs of the two equations intersect once.

When the two lines of the system intersect at exactly one point, it means that the equations have one unique solution, and the system is independent. In this case, the lines have different slopes and different y-intercepts, so they intersect at a single point.

In contrast, if the two lines are parallel and have equal slopes, they will never intersect, indicating that the system has no solution and is inconsistent. Therefore, options A and E are incorrect.