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There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below.
<span>Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.</span>
Case I: 1 Solution
Case 3: Infinite Solutions
This is the most common situation and it involves lines that intersect exactly 1 time.
Case 2: No SolutionsThis only happens when the lines are parallel. As you can see, parallel lines are not going to ever meet.
Example of a stem that has no solution:
Case 3: Infinite Solutions
This is the rarest case and only occurs when you have the same line
Consider, for instance, the two lines below (y = 2x+1 and 2y = 4x +2). These two equations are really the same line .
Example of a system that has infinite solutions: