Types of linear systems
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Types of linear systems can have one solution, no solution, or infinitely many solutions. Systems with one solution have lines that intersect at a single point representing the ordered pair solution. Systems with no solution have parallel lines that never intersect. Systems with infinitely many solutions have lines that are exactly the same, so every point is a solution as the lines always intersect.
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Types of linear systems
- 1. Types of Linear Systems So far during the linear systems unit, we have worked with systems that have one solution. When graphing, you found that solution by looking at where the lines intersect. We also found the solution by substitution. In each method, the solution was given as an ordered pair and represented where the lines of the two equations crossed. Some linear systems have no solution. These systems have lines that never intersect which means the lines are parallel. Look at Case 2 below. Notice that those lines will never touch. This means that there is no solution. The last type of linear system has infinitely many solutions. In this situation, the lines are the exact same, one is graphed directly on top of the other. This means that every point on the line could be a solution because they are always intersecting.