This is a free lesson from our course in Algebra I
In this lesson, you'll 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's 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!
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