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Unit 1.3

Unit 1.3. USE YOUR CALCULATOR!!!. 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. Vocabulary. Substitution method

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Unit 1.3

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  1. Unit 1.3 USE YOUR CALCULATOR!!!

  2. 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.

  3. Vocabulary • Substitution method • Elimination method

  4. 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.

  5. 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)

  6. Try These… • Page 13: 1-3

  7. 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

  8. Ex. • Solve the system using the elimination method. 5x + 7y = 2450 Equation 1 8x + 13y = 4325 Equation 2 • Step 1: Multiply • 5x + 7y = 2450  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

  9. Try These… • Page 14: 6 & 7

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