Answered

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If a system has no solution, how does it look on the graph? What about infinite solutions?

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Azailia

Hi!

If a graph has no solutions, the lines will be parallel.

Lines have "solutions" when they intersect with eachother. If there are no solutions, the lines will not intersect. Only parallel lines don't intersect.

If a graph has infinite solutions, the lines will be the same.

If a line has infinite solutions, they have to constantly be intersecting. That means the lines will have to be directly on top of each other, meaning they will be the same line.

SEE BELOW for graphs. First graph = NO SOLUTIONS; Second graph = INFINITE SOLUTIONS

View image Azailia
View image Azailia

Explanation:

No solution:

  • A graph can only have no solutions if the two lines are parallel. These lines can only be parallel if they have the same slopes, but different y-intercepts. Please check attached graph (1) for illustration of no solution.

Infinitely many solutions:

  • A graph can have infinitely many solutions if the two lines overlap. This can only happen if both the equations are the same or if simplified, are equivalent. Please check attached graph (2 and 3) for illustration of infinitely many solutions.

View image Аноним
View image Аноним
View image Аноним
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