Substitute –2 and –1 for r and s in the first equation
and solve for t.
3-4 Systems of Equations in Three Variables
Solve each system of equations.
11. Therefore, the solution is (–2, –1, 4).
SOLUTION: 12. SOLUTION: Eliminate one variable.
Multiply the first equation by –4 and add with the
second equation.
Eliminate one variable.
Multiply the first equation by 2 and add with the
second equation.
Multiply the third equation by 2, and add with the
second equation.
Multiply the second equation by 2 and the third
equation by 4 then add.
Solve the fourth and fifth equations
.
Solve the fourth and the fifth equation.
Substitute –2 for r in the fifth equation and solve for
s.
This is a false statement. Therefore, there is no
solution.
13. Substitute –2 and –1 for r and s in the first equation
and solve for t.
SOLUTION: eSolutions Manual - Powered by Cognero
Therefore, the solution is (–2, –1, 4).
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Eliminate one variable.
This is a of
false
statement.inTherefore,
there is no
3-4 Systems
Equations
Three Variables
solution.
Eliminate one variable.
Multiply the second equation by –3 and add with the
first equation.
13. SOLUTION: Multiply the second and third equation by 5 and –2
respectively and add.
Eliminate one variable.
Add the first and the third equations.
Solve the fourth and fifth equations.
Multiply the first equation by 3 and add with the
second equation.
Substitute 3 for y in the fourth equation and solve for
x.
Multiply the third equation by –3 and add with the
second equation.
Substitute –1 and 3 for x and y in the first equation
and solve for z.
Since the equations 4, 5 and 6 are same, the system
has an infinite number of solutions.
14. Therefore, the solution is (–1, 3, 7).
SOLUTION: Eliminate one variable.
Multiply the second equation by –3 and add with the
first equation.
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21. AMUSEMENT PARKS Nick goes to the
amusement park to ride roller coasters, bumper cars,
and water slides. The wait for the roller coasters is 1
hour, the wait for the bumper cars is 20 minutes long,
and the wait for the water slides is only 15 minutes
long. Nick rode 10 total rides during his visit.
Because he enjoys roller coasters the most, the
number of times he rode the roller coasters was the
sum of the times he rode the other two rides. If Nick
waited in line for a total of 6 hours and 20 minutes,
how many of each ride did he go on?
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SOLUTION: Let x, y and z be the number of raids in roller
and the wait for the water slides is only 15 minutes
long. Nick rode 10 total rides during his visit.
Because he enjoys roller coasters the most, the
number of
he rodeinthe
rollerVariables
coasters was the
3-4 Systems
oftimes
Equations
Three
sum of the times he rode the other two rides. If Nick
waited in line for a total of 6 hours and 20 minutes,
how many of each ride did he go on?
SOLUTION: Let x, y and z be the number of raids in roller
coaster, bumper car and water slide respectively.
Nick rode 10 rides during his visit.
The number of times that Nick rode the roller coaster
is the sum of the times he rode the other two rides.
So:
Substitute 1 for y in the fifth equation and solve for z.
Nick rode the roller coaster, bumper cars and water
slides 5, 1 and 4 times respectively.
23. FINANCIAL LITERACY Kate invested $100,000
in three different accounts. If she invested $30,000
more in account A than account C and is expected to
earn $6300 in interest, how much did she invest in
each account?
He waited in line for a total of 6 hours 20 minutes.
Substitute x for y + z in the first equation and solve
for x.
SOLUTION: Let a, b and c be the amount invested in the Account
A, B and C respectively.
Kate invested $30,000 more in account A than
account C.
Substitute 5 for x in the second and the third equation
and simplify.
Therefore,
Substitute c + 30000 for a in the first equation and
simplify.
Total interest amount is $6300. That is,
Multiply the fifth equation by –3 and add with the
fourth equation.
.
Substitute c + 30000 for a and simplify.
Substitute 1 for y in the fifth equation and solve for z.
Solve the third and fourth equations.
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Nick rode the roller coaster, bumper cars and water
Page 3
3-4 Systems
of Equations in Three Variables
Solve the third and fourth equations.
–10), (–5, –101), and (6, –90), determine the values
of a, b, and c and write the general form of the
equation.
SOLUTION: Substitute the points (2, –10), (–5, –101), and (6, –
90) in the equation
.
Substitute 25000 for c in the second equation and
solve for a.
Substitute 25000 for c in the third equation and solve
for b.
Solve the equations 1, 2 and 3.
Solve the fourth and fifth equations.
Therefore, she invested $55,000, $20,000 and $25,000
in the account A, B and C respectively.
24. CCSS REASONING Write a system of equations
to represent the three rows of figures below. Use the
system to find the number of red triangles that will
balance one green circle.
Substitute –3 for a in the fourth equation and solve
for b.
SOLUTION: t + c = s, p + t = c, 2s = 3p
where t represents triangle, c represents circle, s
represents square, and p represents pentagon; 5 red
triangles
25. CHALLENGE The general form of an equation for
a parabola is
where (x, y) is a point
on the parabola. If three points on a parabola are (2,
–10), (–5, –101), and (6, –90), determine the values
of a, b, and c and write the general form of the
equation.
SOLUTION: Substitute the points (2, –10), (–5, –101), and (6, –
90) in the equation
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Substitute –3 and 4 for a and b in the first equation.
The value of a, b and c are –3, 4 and –6
respectively.
2
Therefore, the equation of the parabola is y = –3x +
4x – 6.
30. What is the solution of the system of equations
shown below?
.
Page 4
A (0, 3, 3)
respectively.
2
Therefore, the equation of the parabola is y = –3x +
4x – 6.
3-4 Systems of Equations in Three Variables
30. What is the solution of the system of equations
shown below?
Substitute 2 and 5 for x and y in the first equation and
solve for z.
A (0, 3, 3)
B (2, 5, 3)
C no solution
D infinitely many solutions
The solution is (2, 5, 3).
Option B is the correct answer.
31. ACT/SAT The graph shows which system of
equations?
SOLUTION: Eliminate one variable.
Multiply the first equation by 2 and with the second
equation.
A
D B
E Multiply the second equation by 2 and add with the
third equation.
Solve the fourth and fifth equations.
C
Substitute 2 for x in the fourth equation and solve for
y.
SOLUTION: The lines intersect at (3, –2). Substitute the point in
each system of equations.
Substitute 2 and 5 for x and y in the first equation and
solve for z.
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Page 5
3-4 Systems of Equations in Three Variables
First system of equations satisfies the point (3, –2).
Therefore, option A is the correct answer.
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Page 6