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**3.1 Solving Systems by Graphing or Substitution**

Learning Objective: to solve systems using both methods Warm-up (IN) 1. Write each equation in slope intercept form. y=x-9 y=2/5x y=-4/7x+2 y=15x-30 y=3x-3.24

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Notes Linear System – a set of 2 or more equations in 2 or more variables Solution – An ordered pair, (x, y), that satisfies all of the equations Coinciding parallel intersecting Infinitely many solutions no solutions One solution

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Consistent System – Has at least one solution Independent System – Exactly one solution Dependent System – Infinitely many solutions Inconsistent System – no solutions ***To solve by graphing 1 – Graph both lines 2 – Estimate point where they intersect 3 – Check by plugging the point into the 2 equations

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**EX 1 – solve by graphing and classify the system**

Consistent and independent (-1, 3) yes yes

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*****To solve systems by substitution:**

1 – get one variable by itself in one equation 2 – Substitute that expression into the other equation 3 – Solve for the variable 4 – plug that value back into either of the original equations to find the other variable

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**EX 2 – Solve by substitution:**

Always write solution as an ordered pair!!!

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POINT CHALLENGE! Try this… page 158

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**Out – Explain how to use substitution to solve the system**

Summary – today I understood… HW – p #10-17, 25-30, 40-43

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