# 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

### Comments for Systems of Equations - Consistent, Inconsistent, Dependent, or Independent

 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 ----------------------------------------------------- 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

 Dec 02, 2014 Inconsistent Highway signs NEW by: Anonymous A driver is headed north on a long, straight highway and sees this sign: Nearville 150 miles Farville 160 miles Then, surprisingly, an hour later she sees this apparently inconsistent sign on the same highway: Nearville 100 miles Farville 109 miles How can this be possible? Please show ALL work and explanation.

 Oct 07, 2015 3 systems of equations NEW by: Anonymous Can a system of 3 equations and 3 variables be inconsistent and independent at the same time? I do not think so because inconsistent means no solution but independent means 1 solution. Since we are dealing with planes instead of points, do i have this right?

Aug 08, 2020
booooo NEW

# Hello not working well

 Jan 12, 2021 Is this Consistent, Inconsistent, Dependent, or Independent by: Anonymous y=5x+2 5x-y=2