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7-1 Graphing Systems of Equations SWBAT: 1) Solve systems of linear equations by graphing 2) Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent

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What is a System of Equations? A system of equations is two or more equations with the same variables The solution to a system of equations is the ordered pair that is a common solution of all the equations One way we can solve a system of equations is by graphing the equations on the same coordinate plane

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Lets Look at our Packet… They intersect at (2,4), and both have it as a solution.

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Look at another… So they both have (- 1,4) as a solution.

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One more! y = 4/3 x - 4 y = 2/3 x - 6 So they both have (-3,- 8) as a solution.

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Consistent and Independent When two lines intersect, a system of equations has one solution (meaning only one point will satisfy the system). When a system has one solution, the system is said to be consistent and independent.

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Wait…What About? These two lines are parallel! They have same exact slope They will never cross!

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Inconsistent This would occur if the equations never intersect (they are parallel). They have no common coordinates. When a system of equations has no solution, the system is said to be inconsistent.

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What happens here? y = -5x - 2 These two lines the same equation! They are the same exact line!

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Consistent and Dependent This would occur if the equations are the same exact line. All the coordinates are the exact same. So there are infinite solutions. When a system of equations has infinitely many solutions, the system is said to be consistent and dependent.

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Summary…

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Example 2: Solve the system of equations by graphing. Then describe the solution.

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b)

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c)

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