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Solving Linear Systems Algebraically: Substitution and Linear Combination Methods

Learn how to solve systems of equations algebraically using the Substitution and Linear Combination methods, with step-by-step instructions and examples provided.

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Solving Linear Systems Algebraically: Substitution and Linear Combination Methods

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  1. 4.2 Solving Systems Algebraically

  2. The Substitution Method: • 1. Solve one of the equations for one of its____________. • 2. Substitute the expression from Step 1 into the other equation and ______ for the other variable. • 3. ___________ the value from Step 2 into the revised equation from Step 1 and solve. • 4. Write your answer as an _____________. variables solve Substitute ordered pair

  3. Solve the linear system using the substitution method. • 3x – y = 13 2. -x + 3y = 1 2x + 2y = -10 4x+6y=8

  4. The Linear Combination Method: Multiply • 1. _______ one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. • 2. _____ the revised equations from Step 1. Combining like terms will eliminate one of the variables. ________ for the remaining variable. • 3. ___________ the value obtained in Step 2 into either of the original equations and solve for the other variable. Add Solve Substitute

  5. Solve using the linear combination method. 1. 2x – 6y = 19 2. x- 2y = 3 -3x + 2y = 10 2x – 4y = 7

  6. Solve the system of equations by any method. 1. 2x + 3y = -1 2. 6x- 10y = 12 -5x + 5y = 15 -15x + 25y = -30

  7. Solve the system of equations by any method. 3. 4.

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