algebra and trigonometry by cynthia y. young, © 2007 john wiley and sons. all rights reserved....
TRANSCRIPT
Alg
ebra
an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
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hts
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erve
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)
Alg
ebra
an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
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)
Alg
ebra
an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
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
Alg
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rig
on
om
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by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
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erve
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.
Alg
ebra
an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
d.What do equations with three variables What do equations with three variables
look like?look like?
Alg
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on
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by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
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
Alg
ebra
an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
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hts
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erve
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
Alg
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on
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by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
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erve
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
Alg
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an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
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
Alg
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an
d T
rig
on
om
etry
by
Cyn
thia
Y.
Yo
un
g, ©
200
7 J
oh
n W
iley
and
So
ns.
All
rig
hts
res
erve
d.HOMEWORKHOMEWORK
P900-903: 3, 5, 13, 15, 31, 33, 41, 47-49