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Systems of Equations

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What you should be able to answer after learning about systems of equations….. A gym membership at one gym costs $10 every month plus a one-time membership fee of $15, and a gym membership at a another gym costs $4 every month plus a one-time $40 membership fee. After about how many months will the gym membership cost the same amount?

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Definitions A System of Linear Equations consists of two or more linear equations that have the same variables. A Solution of a System of Linear Equations is any order pair that satisfies all the equations. A Consistent System has at least one solution. An Independent System has exactly one solution. A Dependent System has infinitely many solutions. An Inconsistent System has no solution.

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**Special Cases One Point of intersection. One solution Consistent**

Independent Different Slope

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The same line Infinitely many solutions Consistent Dependent Coincident Lines Same slope Same Intercept

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Parellel Lines No Intersection No Solution Inconsistent Same slope Different Y-Intercept

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Steps to find solution Change both equations to slope intercept form (if needed) Graph the lines using the y-intercept and slope. Y = mx + b m = slope b = y – intercept (starting point)

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