Fill in the blank with one of the words or phrases listed below.
system of linear equations solution consistent independent
dependent inconsistent substitution addition
-In a system of linear equations in two variables, if the graphs of the equations are different, the equations are_____________ equations.
A)substitution
B)dependent
C)independent
D)addition

Question

Quizplus · Accepted Answer

If the graphs of the equations are different, it means they do not intersect at any point, which means there is no solution. This makes the system inconsistent. However, if the equations are independent, they will have exactly one solution as long as the system is consistent. Therefore, the best choice is C. If the graphs of the equations are different, it means that they do not intersect, which indicates that there is no common solution. Therefore, the system is inconsistent. Since the system only has 2 variables, it can either be independent or dependent, and it cannot be solved using addition or substitution. However, we cannot determine whether the system is dependent or independent without additional information. Therefore, the best choice is C, which is independent, as it is the stronger condition of the two.

Fill in the Blank with One of the Words or Phrases