Type:Interactive, Lesson Plan
This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Determine if a system of equations has infinite solutions
In this mini-lesson, you will learn how to determine, if a system of equations has infinite solutions. A system of equations has infinite solutions when the lines are parallel, i.e. they have the same slope, and they have the same y-intercept. In fact one equation is a scalar multiple of the other and hence, in effect, the equations represent the same line! Let us look at system of two linear equations Ax + By + C = 0 and Dx + Ey + F = 0: these equations will have infinite solutions if the ratio of A/D, B/E and C/F are the same i.e. A/D = B/E = C/F. In such a case, these lines represent coincident lines, i.e. they overlap at every single point. For example, x + y = 2 and 3x + 3y = 6 have infinite solutions because A/D = B/E = C/F = 1/3. Another way to look at this is: if you multiply line 1 by three you get line 2, and thus these two lines are exactly the same line!
This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.
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- Mathematics > Algebra
- Education > General
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Keywords:equations linear equations infinite solutions algebra online coincident lines slope solving equation multiple ratio systems of equation line practice questions solution quizzes
License Deed:Creative Commons Attribution 3.0