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Published byHomer Robbins Modified over 6 years ago

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Algebra II w/ trig

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Substitution Method: 1. Solve an equation for x or y 2. Substitute your result from step 1 into the other equation and solve for the remaining variable 3. Substitute your result from step 2 into the equation used in step 1 and solve 4. Write your solution as an ordered pair (x, y) 5. Check

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I. Solve each system of linear equations by using substitution. A. B.

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C. D.

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Elimination Method: 1. Arrange each equation in Standard form, Ax + By =C 2. Multiply one or both equations by a real number so that when the equations are added together one variable will cancel out. 3. Add the 2 equations together. Solve for the remaining variable. 4. Substitute the value form step 3 into one of the original equations and solve for the other variable. 5. Write the solution as an ordered pair (x, y) 6. check

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II. Solve each system of linear equations by using elimination. A. B.

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C. D.

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3.5 Solving Systems of Equations in Three Variables The solution to systems of equations in three variables is an ordered triple (x, y, z) that makes all 3 equations true. 3 Possible Solutions: A unique solution Infinitely many solutions No solution

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Steps for Solving in 3 Variables (Most of the Time) 1. Using the 1st 2 equations, cancel one of the variables. 2. Using the last 2 equations, cancel the same variable from step 1. 3. Use the results of steps 1 & 2 to solve for the 2 remaining variables. 4. Plug the results from step 3 into one of the original 3 equations and solve for the 3rd remaining variable. 5. Write the solution as an ordered triple (x,y,z).

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Solve the system: A.

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B.

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C.

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D.

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E.

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