 # Algebra II w/ trig. 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.

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Algebra II w/ trig

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

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

C. D.

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

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

C. D.

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

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).

Solve the system: A.

B.

C.

D.

E.

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