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Systems of Equations - Consistent, Inconsistent, Dependent, or Independent
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Systems of Equations - Consistent, Inconsistent, Dependent, or Independent











































Identify each of the following systems of equations as: Consistent, Inconsistent, Dependent, or Independent.


System “A”

x + 2y = 12
x - 2y = 2


System “B”


3x - y = -5
3x - y = 10


System “C”

2r + 5t = -20
3r - 5t = 10


System “D”

3p + 3q = 15
6p + 6q = 30

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Jul 04, 2012
Consistent, Inconsistent, Dependent, or Independent Systems of Equations
by: Staff

The answer:


Definitions:

SYSTEM of linear EQUATIONS: a group of two or more linear equations which have the same variables. An example is shown below:

x + 2y = 14
2x + y = 6


INDEPENDENT SYSTEM of equations: none of the equations in the system can be derived from any of the other equations in the system. The example shown above is a good example of an Independent System.


DEPENDENT SYSTEM: at least one of the equations in the system can be derived from the other equations in the system. There are an infinite number of solutions for a Dependent System. There is not enough information to find a single, unique solution. Graphically, dependent systems are the same line.


The 1st example below is a Dependent System. The second equation is 3 times the first equation:

x + 2y = 14
3x + 6y = 42


The 2nd example below is also a Dependent System. The third equation is the sum of the first two equations:

x + 2y + z = 14
3x + 6y + 5z = 42
4x + 8y + 6z = 56



CONSISTENT linear system: A consistent system has AT LEAST ONE SOLUTION. Two examples are shown below:

1st example – there is only one solution

x + 2y = 14
2x + y = 6


2nd example – there are an infinite number of solutions because a graph of both equations shows that one line falls on top of the other.

x + 2y = 14
3x + 6y = 42


INCONSISTENT linear systems: NO SOLUTIONS at all. Graphically, inconsistent systems are parallel lines. An example of on inconsistent system is shown below. There is no solution for x and y because the lines are parallel.

y = 3x + 5
y = 3x + 10


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System “A”

x + 2y = 12
x - 2y = 2

System “A” is a “Consistent” linear system because there is at least one solution.

System “A” is an “Independent” linear system because neither of the equations in the system can be derived from the other equation.



System “B”


3x - y = -5
3x - y = 10


System “B” is an INCONSISTENT linear system. There are NO SOLUTIONS for x and y. Graphically, the two equations are parallel lines.


System “B” is an “Independent” system because neither of the equations in the system can be derived from the other equation.



System “C”

2r + 5t = -20
3r - 5t = 10

System “C” is a “Consistent” linear system because there is at least one solution.


System “C” is an “Independent” system because neither of the equations in the system can be derived from the other equation.



System “D”

3p + 3q = 15
6p + 6q = 30


System “D” is a “Consistent” linear system because there is at least one solution.

System “D” is a “Dependent” system because the second equation can be derived from the first equation.



Thanks for writing.

Staff
www.solving-math-problems.com


Feb 17, 2014
help me solve
by: frustrated

doing chapter on consistent and inconsistent systems....can anyone help me solve

3/5x - 8/3y = -105

2/3x - 4/9y = -26

and please show work

thank you

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