Question

A consistent system of equations is a system with __________. A. the same line B. parallel lines C. intersecting lines and lines that have the same slope D. intersecting lines and lines that have the same equation

Answer 1

It's D. intersecting lines and lines that have the same equation. 

Answer 2

A system of two linear equations can have unique solution, infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions.

• If a system has at least one solution, it is said to be consistent.
• If a consistent system has unique solution, it is independent.
• If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line.
• If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Therefore, consistent system of equations has one solution (intersecting lines) or infinitely many solutions (the same line).

Answer: correct choice is D.