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WorksheetsSolving Equations in Three Variables
Total questions: 22
Worksheet time: 2hrs 22mins
Name
Class
Date
1.
Solve the system of equations:
a)
( 5, 1, -4)
b)
(-5, 3, -1)
c)
None of these
d)
( -1, 5, -4)
2.
Solve the system of equations:
a)
( -2, 4, 3)
b)
( 2, 1, 6)
c)
None of these
d)
infinite # of solutions
3.
Solve the system.
a)
(3, -2, 4)
b)
(2, -3, 1)
c)
(-3, 2, -1)
d)
Infinitely many solutions
4.
Solve the system.
a)
(2, -2, 3)
b)
(2, 1, 4)
c)
(-2, 2, -3)
d)
No Solution
5.
Solve the system.
a)
(5, -6, 3)
b)
(2, 3, -1)
c)
(-4, 2, 5)
d)
No Solution
6.
Determine which ordered triple is a solution of the systems of equations?
2x+y=0
x+3y-z=-11
7x+5y+4z=21
2x+y=0
x+3y-z=-11
7x+5y+4z=21
a)
(0,0,11)
b)
(1,-2,6)
c)
(-1,2,-16
d)
(0,1,-14)
7.
Solve the system of equations.
x-3y=13
5x+6z=41
2x+4y-z=5
x-3y=13
5x+6z=41
2x+4y-z=5
a)
(7,-2,1)
b)
(13,0,-4)
c)
(10,-1,11)
d)
(1,-4,6)
8.
The solution of a system of three linear equations in three variables, x,y, and z, is called a(n) ___________________ (x,y,z).
a)
Ordered Pair
b)
Integer
c)
Ordered Triple
d)
Sum
9.
Determine which ordered triple is a solution of the systems of equations?
2x+y=0
x+3y-z=-11
7x+5y+4z=21
2x+y=0
x+3y-z=-11
7x+5y+4z=21
a)
(0,0,11)
b)
(1,-2,6)
c)
(-1,2,-16
d)
(0,1,-14)
10.
Solve the system of equations.
x-3y=13
5x+6z=41
2x+4y-z=5
x-3y=13
5x+6z=41
2x+4y-z=5
a)
(7,-2,1)
b)
(13,0,-4)
c)
(10,-1,11)
d)
(1,-4,6)
11.
Solve the system of equations:
a)
( -2, 3, -3)
b)
None of these
c)
( -2, -3, 3)
d)
( -3, 3, -2)
12.
What is your solution if your variables go away and you are left with 0 = 0?
a)
No Solution
b)
All Real Numbers
c)
Infinitely Many Solutions
d)
(x, y, z)
13.
What are systems of linear equations?
a)
a set of two or more linear equations in the same variables
b)
a polynomial with three terms
c)
set of two or more linear inequalities in the same variables
14.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
15.
The solution of a system of three linear equations in three variables, x,y, and z, is called a(n) ___________________ (x,y,z).
a)
Ordered Pair
b)
Integer
c)
Ordered Triple
d)
Sum
16.
CHALLENGE: Three equations.
x + y + z = 4
x = -2y
z = -3y
Solve the system of equations using substitution.
x + y + z = 4
x = -2y
z = -3y
Solve the system of equations using substitution.
a)
x = 2
y = -1
z = 3
y = -1
z = 3
b)
x= -5
y = 3
z = 1
y = 3
z = 1
c)
x = 10
y = -2
z = 0
y = -2
z = 0
d)
x= 4
y = 1
z = -1
y = 1
z = -1
17.
CHALLENGE: Three equations.
x + y + z = 4
x = -2y
z = -3y
Solve the system of equations using substitution.
x + y + z = 4
x = -2y
z = -3y
Solve the system of equations using substitution.
a)
x = 2
y = -1
z = 3
y = -1
z = 3
b)
x= -5
y = 3
z = 1
y = 3
z = 1
c)
x = 10
y = -2
z = 0
y = -2
z = 0
d)
x= 4
y = 1
z = -1
y = 1
z = -1
18.
Solve the system of equations:
a)
( -2, 3, -3)
b)
None of these
c)
( -2, -3, 3)
d)
( -3, 3, -2)
19.
Solve the system of equations:
a)
( 4, 0, -2)
b)
( -4, -2, 0)
c)
None of these
d)
( -4, 0, -2)
20.
Solve the system of equations:
a)
( 4, 2, -1)
b)
( 4, 3, -1)
c)
None of these
d)
( -4, 3, 1)
21.
Solve the system.
a)
(3, -9, 2)
b)
(3, -2, 9)
c)
(2, 3, -1)
d)
No Solution
22.
Solve the system.
a)
(1/2, 4, -2)
b)
(3, 3/2, -1/2)
c)
(-1, 6, -4)
d)
Infinitely many solutions
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