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Unit 1.3 USE YOUR CALCULATOR!!!

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**Unit 1 – Algebra: Linear Systems, Matrices, & Vertex-Edge Graphs**

1.3 – Solve Linear Systems Algebraically Georgia Performance Standard: MM3A5c – Represent and solve realistic problems using systems of linear equations.

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Vocabulary Substitution method Elimination method

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**So what’s up with the Substitution Method?**

Step 1: Solve one of the equations for one of it’s variables Step2: Plug in what you found into the other equation Step 3: Substitute what you got from Step 2 into either of the original equations and solve for the other variable.

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**Ex. Solve the system using the substitution method.**

y + 3x = 5 Equation 1 y -2x = -5 Equation 2 Step 1: Solve Equation 2 for y y= 2x - 5 Step 2: Substitute result for y into Equation 1 & solve (2x-5) + 3x = 5 x= 2 Step 3: Plug the value of x into the revised Equation from Step 1 and solve for y. y= 2(2) – 5 y= -1 Solution: (2,-1)

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Try These… Page 13: 1-3

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**So what’s up with the Elimination Method?**

Step 1: Multiply one or both of the equations by a constant to get coefficients that differ only in sign for one of the variables Step2: Add revised equations from Step 1 and solve for remaining variable Step 3: Substitute the value from Step 2 into either of the original equations and solve for the other variable

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**Ex. Solve the system using the elimination method.**

5x + 7y = Equation 1 8x + 13y = Equation 2 Step 1: Multiply 5x + 7y = multiply by -8 8x + 13y = 4325 multiply by -5 y= 225 Step 2: Substitute result for y into one of the original equations 5x + 7(225) = 2450 x= 175 X = 175, Y = 225

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Try These… Page 14: 6 & 7

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