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Classifying Systems of Linear Equations Types of Systems There are 3 different types of systems of linear equations 3 Different Systems: 1) Consistent-independent 2) Inconsistent 3) Consistent-dependent Type 1: Consistent-independent A system of linear equations having exactly one solution is described as being consistentindependent. y The system has exactly one solution x at the point of intersection Type 2: Inconsistent A system of linear equations having no solutions is described as being inconsistent. y The system has no solution, the x lines are parallel Remember, parallel lines have the same slope Type 3: Consistent-dependent A system of linear equations having an infinite number of solutions is described as being consistent-dependent. y The system has infinite solutions, x the lines are identical So basically…. If the lines have the same y-intercept b, and the same slope m, then the system is consistent-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-independent Example 1 x + 5y = 9 3x – 2y = 12 (1) To solve, rewrite each equation in the (2) form y = mx +b Isolating y in line (1) x + 5y = 9 5y = -x + 9 x 9 y 5 1 9 y x 5 5 Isolating y in line (2) 3x – 2y = 12 -2y = -3x + 12 3 x 12 y 2 3 y x6 2 What type of system is it? 1 9 y x 5 5 What is the slope and y-intercept for line (1)? 1 m 5 9 b 5 y 3 x6 2 What is the slope and y-intercept for line (2)? 3 m 2 b 6 Since the lines have different slopes they will intersect. The system will have one solution and is classified as being consistent-independent. Questions? Any Questions? Homework: #1,2,3 – 17 odd numbers only