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Let’s check out your problem:
Solve the
system of equations
by substitution.
\newline
x
+
y
+
2
z
=
−
1
x + y + 2z = -1
x
+
y
+
2
z
=
−
1
\newline
y
=
−
6
y = -6
y
=
−
6
\newline
−
2
x
+
y
+
2
z
=
−
4
-2x + y + 2z = -4
−
2
x
+
y
+
2
z
=
−
4
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Math Problems
Algebra 2
Solve a system of equations in three variables using substitution
Full solution
Q.
Solve the system of equations by substitution.
\newline
x
+
y
+
2
z
=
−
1
x + y + 2z = -1
x
+
y
+
2
z
=
−
1
\newline
y
=
−
6
y = -6
y
=
−
6
\newline
−
2
x
+
y
+
2
z
=
−
4
-2x + y + 2z = -4
−
2
x
+
y
+
2
z
=
−
4
Substitute
y
=
−
6
y = -6
y
=
−
6
:
Substitute
y
=
−
6
y = -6
y
=
−
6
into the first equation
x
+
y
+
2
z
=
−
1
x + y + 2z = -1
x
+
y
+
2
z
=
−
1
.
\newline
x
+
(
−
6
)
+
2
z
=
−
1
x + (-6) + 2z = -1
x
+
(
−
6
)
+
2
z
=
−
1
\newline
x
−
6
+
2
z
=
−
1
x - 6 + 2z = -1
x
−
6
+
2
z
=
−
1
Add
6
6
6
to isolate x:
Add
6
6
6
to both sides to isolate
x
+
2
z
x + 2z
x
+
2
z
.
\newline
x
+
2
z
=
−
1
+
6
x + 2z = -1 + 6
x
+
2
z
=
−
1
+
6
\newline
x
+
2
z
=
5
x + 2z = 5
x
+
2
z
=
5
Substitute
y
=
−
6
y = -6
y
=
−
6
:
Substitute
y
=
−
6
y = -6
y
=
−
6
into the third equation
−
2
x
+
y
+
2
z
=
−
4
-2x + y + 2z = -4
−
2
x
+
y
+
2
z
=
−
4
.
\newline
−
2
x
+
(
−
6
)
+
2
z
=
−
4
-2x + (-6) + 2z = -4
−
2
x
+
(
−
6
)
+
2
z
=
−
4
\newline
−
2
x
−
6
+
2
z
=
−
4
-2x - 6 + 2z = -4
−
2
x
−
6
+
2
z
=
−
4
Add
6
6
6
to isolate
−
2
x
-2x
−
2
x
:
Add
6
6
6
to both sides to isolate
−
2
x
+
2
z
-2x + 2z
−
2
x
+
2
z
.
\newline
−
2
x
+
2
z
=
−
4
+
6
-2x + 2z = -4 + 6
−
2
x
+
2
z
=
−
4
+
6
\newline
−
2
x
+
2
z
=
2
-2x + 2z = 2
−
2
x
+
2
z
=
2
Divide by
−
2
-2
−
2
to solve
x
x
x
:
Divide the entire equation by
−
2
-2
−
2
to solve for
x
x
x
.
x
=
2
−
2
x = \frac{2}{-2}
x
=
−
2
2
x
=
−
1
x = -1
x
=
−
1
More problems from Solve a system of equations in three variables using substitution
Question
Solve using substitution.
5
x
−
2
y
=
−
7
5x - 2y = -7
5
x
−
2
y
=
−
7
x
=
−
5
x = -5
x
=
−
5
(_,_)
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Question
Is
(
1
,
1
)
(1,1)
(
1
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)
a solution to this system of equations?
\newline
4
x
+
10
y
=
14
4x + 10y = 14
4
x
+
10
y
=
14
\newline
x
+
6
y
=
7
x + 6y = 7
x
+
6
y
=
7
\newline
Choices:
\newline
(A) yes
\newline
(B) no
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Question
Which describes the system of equations below?
\newline
y
=
–
3
x
+
9
y = –3x + 9
y
=
–3
x
+
9
\newline
y
=
–
3
x
+
9
y = –3x + 9
y
=
–3
x
+
9
\newline
Choices:
\newline
(A) consistent and independent
\text{(A) consistent and independent}
(A) consistent and independent
\newline
(B) consistent and dependent
\text{(B) consistent and dependent}
(B) consistent and dependent
\newline
(C) inconsistent
\text{(C) inconsistent}
(C) inconsistent
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Question
Solve using elimination.
\newline
7
x
−
8
y
=
−
17
7x - 8y = -17
7
x
−
8
y
=
−
17
\newline
−
7
x
+
3
y
=
2
-7x + 3y = 2
−
7
x
+
3
y
=
2
\newline
(
_
_
_
_
,
_
_
_
_
)
(\_\_\_\_, \_\_\_\_)
(
____
,
____
)
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Question
Solve.
\newline
x
=
−
2
x = -2
x
=
−
2
\newline
−
2
x
+
2
y
=
−
8
-2x + 2y = -8
−
2
x
+
2
y
=
−
8
\newline
(
_
_
_
_
,
_
_
_
_
)
(\_\_\_\_, \_\_\_\_)
(
____
,
____
)
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Posted 10 months ago
Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases
3
3
3
hot dog meals and
3
3
3
hamburger meals, paying a total of
$
36
\$36
$36
. Mr. Hogan buys
1
1
1
hot dog meal and
3
3
3
hamburger meals, spending
$
26
\$26
$26
in all. How much do the meals cost?
\newline
Hot dog meals cost
$
\$
$
_______ each, and hamburger meals cost
$
\$
$
________ each.
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Posted 10 months ago
Question
Solve the system of equations by substitution.
\newline
−
3
x
−
y
−
3
z
=
−
11
-3x - y - 3z = -11
−
3
x
−
y
−
3
z
=
−
11
\newline
z
=
5
z = 5
z
=
5
\newline
x
−
y
+
3
z
=
19
x - y + 3z = 19
x
−
y
+
3
z
=
19
\newline
(____.____,____)
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Posted 6 months ago
Question
Solve the system of equations by elimination.
\newline
x
−
3
y
−
2
z
=
10
x - 3y - 2z = 10
x
−
3
y
−
2
z
=
10
\newline
3
x
+
2
y
+
2
z
=
14
3x + 2y + 2z = 14
3
x
+
2
y
+
2
z
=
14
\newline
2
x
−
3
y
−
2
z
=
16
2x - 3y - 2z = 16
2
x
−
3
y
−
2
z
=
16
\newline
(
_
,
_
,
_
)
(\_,\_,\_)
(
_
,
_
,
_
)
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Posted 6 months ago
Question
Solve the system of equations.
\newline
y
=
x
2
+
36
x
+
3
y = x^2 + 36x + 3
y
=
x
2
+
36
x
+
3
\newline
y
=
22
x
−
37
y = 22x - 37
y
=
22
x
−
37
\newline
Write the coordinates in exact form. Simplify all fractions and radicals.
\newline
(
_
,
_
)
(\_,\_)
(
_
,
_
)
\newline
(
_
,
_
)
(\_,\_)
(
_
,
_
)
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Posted 6 months ago
Question
Solve the system of equations.
\newline
y
=
−
x
−
24
y = -x - 24
y
=
−
x
−
24
\newline
x
2
+
y
2
=
488
x^2 + y^2 = 488
x
2
+
y
2
=
488
\newline
Write the coordinates in exact form. Simplify all fractions and radicals.
\newline
(
_
,
_
)
(\_,\_)
(
_
,
_
)
\newline
(
_
,
_
)
(\_,\_)
(
_
,
_
)
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Posted 6 months ago
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