Lesson Equations with up to 2 solutions

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This Lesson (Equations with up to 2 solutions) was created by by Shin123(626) About Me : View Source, Show
About Shin123: Just a kid who solves math problems for fun :)
A system of 2 equations can have 2 solutions, for x and y,no solutions, or infinite solutions. Example,
system%28y=4x-5%2C4x-y=8%29 Substitute 4x-5 for y,
4x-%284x-5%29=8
4x-4x%2B5=8
5=8 This is a false statement so there are no solutions. This graph shows,
graph%28450%2C450%2C-10%2C10%2C-10%2C10%2Cy=4x-5%2Cy=8%2B4x%29 As you can see, the two lines are parallel to each other so they will never meet so there is no solution.
system%284x%2B6y=16%2C5x-2y=1%29 Multiply the top by 5 and the bottom by 4,
system%2820x%2B30y=80%2C20x-8y=4%29 Subtract the 2 equations,
38y=76 highlight%28y=2%29 Substitute 2 for y,
4x%2B12=16 4x=4 highlight%28x=1%29 The lines intersect at the point (1,2) in the following graph,
graph%28450%2C450%2C-10%2C10%2C-10%2C10%2Cy=8%2F3-%282%2F3%29x%2Cy=%285%2F2%29x-1%2F2%29
system%28y=3x%2C6x-2y=0%29 Substitute 3x for y,
6x-6x=0
0=0 Infinite amount of solutions.
graph%28450%2C450%2C-10%2C10%2C-10%2C10%2Cy=3x%2Cy=3x%29 As you can see, the 2 lines intersect. To learn more about graphs, check out this lesson.
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