Determine if a systems of equations has no solution

Algebra I: Determine if a systems of equations has no solution

This is a free lesson from our course in Algebra I


	In this lesson, we'll explain how to find out whether a system of equations has no solution. In a system of two linear equations Ax + By + C = 0 and Dx + Ey + F = 0, the only circumstance in which the system of equation would have no solution is when the lines are parallel, i.e. they have the same slope and they don't overlap. Then there can be no points that are common to both lines. In case of this system of two linear equations, the two lines are parallel if A/B = D/E. For example, 5x - 3y = 1 and 15x - 9y = 5 have no solution because A/B = D/E = -5/3. (More text below video...)

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(Continued from above) For example, Solve the system of linear equations.
4x - y = 8
-8x + 2y = -5
Steps to solve this example:
• multiply all terms in the first equation by 2,
8x - 2y = 16
-8x + 2y = -5
• add the two equations
0x + 0y = 11 or 0 = 11
• conclusion: Because there are no values of x and y for which 0x + 0y = 11, the given system of equations has no solutions. This system is inconsistent.

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