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d.Solving Systems of EquationsSolving Systems of Equations

Solve the system:

2 14

3 4 9

4 6 3 13

x

x y

x y z

(7,3,1)

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d.Solving Systems of EquationsSolving Systems of Equations

Solve the system:

2 4 8

3 2 12

1

x z

x z

x y z

(2,-6,3)

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d.What about this one?What about this one?

Solve the system:

2 3 1

0

3 3 2 1

x y z

x y z

x y z

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d.

Solving Systems of Linear EquationsSolving Systems of Linear Equationswith Three Variables Usingwith Three Variables UsingElimination and SubstitutionElimination and Substitution

Step 1: Reduce the system to two equations in two variables using elimination.

Step 2: Solve the resulting system of two equations using elimination or substitution.

Step 3: Substitute the solutions in Step 2 into any of the original equations and solve for the third variable.

Step 4: Check the solution in each of the three original equations.

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d.What do equations with three variables What do equations with three variables

look like?look like?

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d.Your Turn!Your Turn!

Click mouse to continueClick mouse to continue

Solve the system:

2 3 1

0

3 3 2 1

x y z

x y z

x y z

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d.Your Turn!Your Turn!

1233 :3 Equation

0 :2 Equation

132 :1 Equation

zyx

zyx

zyx

123

0 2 equation

132 1 equation Add

yEliminate

zx

zyx

zyx

Click mouse to continue with answerClick mouse to continue with answer

279

1233 3 equation

3936 1 equation times 3 Add

zx

zyx

zyx

Answer 1 of 3

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d.Your Turn!Your Turn!

1

279 279

369 123

system. variable two the from Eliminate

z

zxzx

zxzx

x

Click mouse to continue with answerClick mouse to continue with answer

1

2 33

011 1123x

for solve to back Substitue . for solve to back Substitute

x

yx

y

y.x

Answer 2 of 3

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d.Your Turn!Your Turn!

Check that 1, 2, 1 satisfy all three equations

2 1 2 3 1 1

1 2 1 0

3 1 3 2 2 1 1

( 1,2,1)

x y z

Answer 3 of 3

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d.HOMEWORKHOMEWORK

P900-903: 3, 5, 13, 15, 31, 33, 41, 47-49