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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: Consistent Inconsistent dependent

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**Type 1: Consistent-independent**

A system of linear equations having exactly one solution is described as being consistent. y The system has exactly one solution at the point of intersection x

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

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

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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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If each equation in a system of equations is linear, then we have a system of linear equations.

If each equation in a system of equations is linear, then we have a system of linear equations.

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