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Classifying Systems of Linear Equations afridiimran94@yahoo.com

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Types of Systems There are 3 different types of systems of linear equations 3 Different Systems: 1) Consistent 2) Inconsistent 3) dependent

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Type 1: Consistent-independent A system of linear equations having exactly one solution is described as being consistent. y x The system has exactly one solution at the point of intersection

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Type 2: Inconsistent A system of linear equations having no solutions is described as being inconsistent. y x The system has no solution, the lines are parallel Remember, parallel lines have the same slope

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Type 3: Consistent-dependent A system of linear equations having an infinite number of solutions is described as being dependent. y x The system has infinite solutions, the lines are identical

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So basically…. If the lines have the same y-intercept b, and the same slope m, then the system is dependent If the lines have the same slope m, but different y-intercepts b, the system is inconsistent If the lines have different slopes m, the system is consistent

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Example 1 x + 5y = 9 3x – 2y = 12 (1) (2) To solve, rewrite each equation in the form y = mx +b Isolating y in line (1)Isolating y in line (2) x + 5y = 9 5y = -x + 9 3x – 2y = 12 -2y = -3x + 12

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What type of system is it? What is the slope and y-intercept for line (1)? What is the slope and y-intercept for line (2)? Since the lines have different slopes they will intersect. The system will have one solution and is classified as being consistent.

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