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Let’s check out your problem:
Which describes the
system of equations
below?
\newline
y
=
5
2
x
+
9
5
y = \frac{5}{2}x + \frac{9}{5}
y
=
2
5
x
+
5
9
\newline
y
=
5
2
x
+
5
4
y = \frac{5}{2}x + \frac{5}{4}
y
=
2
5
x
+
4
5
\newline
Choices:
\newline
(A)consistent and dependent
\newline
(B)inconsistent
\newline
(C)consistent and independent
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Math Problems
Grade 8
Classify a system of equations
Full solution
Q.
Which describes the system of equations below?
\newline
y
=
5
2
x
+
9
5
y = \frac{5}{2}x + \frac{9}{5}
y
=
2
5
x
+
5
9
\newline
y
=
5
2
x
+
5
4
y = \frac{5}{2}x + \frac{5}{4}
y
=
2
5
x
+
4
5
\newline
Choices:
\newline
(A)consistent and dependent
\newline
(B)inconsistent
\newline
(C)consistent and independent
Determine System Type:
To determine the type of system, we need to compare the slopes and
y
y
y
-intercepts of the two equations.
Slope-Intercept Form:
The
slope-intercept form
of a line is
y
=
m
x
+
b
y = mx + b
y
=
m
x
+
b
, where
m
m
m
is the
slope
and
b
b
b
is the
y-intercept
.
First Equation Analysis:
For the first equation
y
=
5
2
x
+
9
5
y = \frac{5}{2}x + \frac{9}{5}
y
=
2
5
x
+
5
9
, the slope (
m
m
m
) is
5
2
\frac{5}{2}
2
5
and the y-intercept (
b
b
b
) is
9
5
\frac{9}{5}
5
9
.
Second Equation Analysis:
For the second equation
y
=
5
2
x
+
5
4
y = \frac{5}{2}x + \frac{5}{4}
y
=
2
5
x
+
4
5
, the slope (
m
m
m
) is also
5
2
\frac{5}{2}
2
5
and the y-intercept (
b
b
b
) is
5
4
\frac{5}{4}
4
5
.
Parallel Lines
Conclusion:
Since both equations have the same slope but different
y
y
y
-intercepts, the lines are parallel and will never intersect.
Inconsistent System:
Parallel lines that never intersect mean that there is no solution to the system of equations, making it inconsistent.
More problems from Classify a system of equations
Question
Solve using substitution.
5
x
−
2
y
=
−
7
5x - 2y = -7
5
x
−
2
y
=
−
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x
=
−
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x = -5
x
=
−
5
(_,_)
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Question
Is
(
1
,
1
)
(1,1)
(
1
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1
)
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 8 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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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 5 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 5 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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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 5 months ago
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