A consistent system of equations is a system with __________.
the same line
parallel lines
intersecting lines and lines that have the same slope
intersecting lines and lines that have the same equation
A consistent system of equations is a system with intersecting lines. In other words, it is a system of equations where the lines represented by each equation intersect at a single point. This means that the system has a solution, and that solution represents the coordinates of the intersection point of the lines.
To check if a system of equations is consistent, you can solve the system by various methods such as substitution, elimination, or matrix operations. If the resulting solution represents a valid point of intersection, then the system is consistent. If there is no valid solution or the lines are parallel, the system is said to be inconsistent.
So, to determine if a system of equations is consistent, you need to solve the equations and check if the solution exists and represents a single point of intersection.