Transcript CHAPTER 6

Solve the system:
 2 x  14
3x  4 y  9
 4 x  6 y  3 z  13
(7,3,1)
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Solving Systems of Equations
Solve the system:
2 x  4 z  8
3 x  2 z  12
x  y  z  1
(2,-6,3)
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Solving Systems of Equations
Solve the system:
2 x  y  3 z  1
x yz 0
3x  3 y  2 z  1
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
What about this one?
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.
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Solving Systems of Linear Equations
with Three Variables Using
Elimination and Substitution
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
What do equations with three variables
look like?
Solve the system:
2 x  y  3 z  1
x yz 0
3x  3 y  2 z  1
Click mouse to continue
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Your Turn!
Equation 1 : 2 x  y  3z  1
Equation 2 : x  y  z  0
Equation 3  : 3 x  3 y  2z  1
Eliminate y
Add equation 1
equation 2
2 x  y  3z  1
xy z 0
3 x  2z  1
Add 3 times equation 1
equation 3
6 x  3y  9z  3
3 x  3y  2z  1
9 x  7z  2
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Answer 1 of 3
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Your Turn!
Eliminate x from the two variable system.
3 x  2z  1
 9 x  6z  3
9 x  7z  2
9 x  7z  2
z 1
Substitute back to solve for x.
3x  21  1
3 x  3
x  1
Substitue back to solve for y.
 1 y  1  0
y 2
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Answer 2 of 3
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Your Turn!
Check that x  1, y  2, z  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)
Answer 3 of 3
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
Your Turn!
 P900-903: 3, 5, 13, 15, 31, 33, 41, 47-49
Algebra and Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved.
HOMEWORK