October 15, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Determine if a systems of equations has no solution.

In this mini-lesson, we 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 the above 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.

In this mini-lesson, we 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 the above 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.

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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Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Use appropriate tools strategically.

Attend to precision.

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.