Question

A consistent, independent system of equations is a system with ________.

A. Intersecting lines that have different slopes and different y-intercepts.

B. Intersecting lines that have the same slope and same y-intercepts.

C. Intersecting lines that have the same slope but different y-intercepts.

D. Only one line.

Answer 1

A consistent, independent system of equations is represented by intersecting lines that have different slopes and different y-intercepts, which corresponds to option A.

Step-by-step explanation:

A consistent, independent system of equations is a system with intersecting lines that have different slopes and different y-intercepts. The correct answer is A. Lines with different slopes guarantee that they will intersect only once, creating one solution for the system, which makes it both consistent and independent. On the other hand, lines with the same slope but different y-intercepts (option C) would never intersect, making the system inconsistent. Lines with the same slope and same y-intercepts (option B) coincide with each other, making the system dependent. Option D describes only one line, so there's no system to speak of.

Answer 2

Option A. Intersecting lines that have different slopes and different y-intercepts.

Step-by-step explanation:

we know that

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

If a system has at least one solution, it is said to be consistent

If a consistent system has exactly one solution, it is independent

If we have intersecting lines that have different slopes and different y-intercepts

then

will have one solution

therefore

The system will be consistent independent