Equivalent equations are equations that have the same solution set.
There is no special name. Two totally unrelated equations could have the same solution(s).
The statement - The graph of a system of equations with the same slope and the same y intercepts will have no solution is True
Consistent equations are two or more equations that have the same solution.
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.