How do you know if a linear system is consistent or inconsistent?

Two curves are consistent if it is possible for some point to be on both. (Being on one curve is consistent with being on the other.) There is an intersection. (Possibly many intersections.)

Two curves are inconsistent is it is impossible for any point to be on both. (Being on one curve is inconsistent with being on the other -- it contradicts, being on the other.) There is no intersection.

Statements are consistent if it is possible for both to be true, statements are inconsistent if it is not possible for both to be true. (The truth of one is consistent or inconsistent with the truth of the other.)

How many kinds of solutions are there?

Answer:

From the category in which this question is asked, I will assume you mean a finite linear system of equations. If such a system is in#n#variables, then there are#n + 2#kinds of solutions.

Explanation:

If a linear system involves#n#variables,#x_1, x_2,..x_n#, then the solution set will take one of the following#n + 2#forms:

(0) The empty set. The system is inconsistent and has no solutions.
(1) A unique solution in the form of an#n#-tuple
(2) A line of solutions expressible as:

#x_1 = a_1*t + b_1#
#x_2 = a_2*t + b_2#
...
#x_n = a_n*t + b_n#

for all#t in RR#

(3) A plane of solutions expressible as:

#x_1 = a_1*t_1 + b_1*t_2 + c_1#
#x_2 = a_2*t_1 + b_2*t_2 + c_2#
...
#x_n = a_n*t_1 + b_n*t_2 + c_n#

for all#(t_1, t_2) in RR xx RR#

...
(n+1) The whole of#RR^n#

George C. · 1 · Jun 22 2015

What are consistent and inconsistent systems?

A system of equations is said to be consistent if it has at least one solution; otherwise, it is inconsistent.

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I hope that this was helpful.

Wataru · 1 · Nov 25 2014

Questions

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• What are consistent and inconsistent systems?

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• What kind of solutions does #3x-4y=13# and #y=-3x-7# have?

• How do you know if the system #3x+2y=4# and #-2x+2y=24# is consistent or inconsistent?

• How many solutions do the system of equations #2x-3y=4# and #4x-6y =-7# have?

• How do you know if #x+2y=4# and #2x+4y=5# is consistent or inconsistent?

• How do you determine how many solutions #x=2# and #2x+y=1# has?

• How do you know when a system of equations is inconsistent?

• How do you know when a system of equations has no solution?

• How do you write a system of equations with one solution, a system of equations with no solution and a system of equations with infinitely many solutions?

• How do you write a system of equations with one solution, a system of equations with no solution and a system of equations with infinitely many solutions?

• What kind of solutions does #3x + 2y = 4# and #2x - y = 5# have?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x - y = -2 and -4x + 2y= 5?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y = x + 3 and y = –2x + 3?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y = x + 2 and –4x + y = –1 ?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 2 + y = 2x and y – 2x = 5?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given x - 4y = 2 and 2x - 8y = 5?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y = 1/3x - 2 and y = -x -6?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x-5y= -17 and -2x+y=6?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-8y=0 and -2x+5y=-2?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 4x-6y=2 and 5x+3y= 1?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 2x-5y=3 and -4x+10y= -6?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 5x+ 4y= -18 and 2x+3y=-24?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 2x + 3y= -6 and 3x- 4y= 25?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 4x- 3y= 8 and -8x +6y= 16?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 7x+5y= -12 and 3x-4y=1?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given -5x+3y= -5 and y= 5/3x + 1?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given x-2y=2 and 2x-y= -5?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-y= -4 and x+ 3y= -28?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 6x +y= -6 and 4x+3y= 17?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x-2y= 10 and -6x +4y= -20?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 2x +3y= 17 and 5x+8y= 20?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y=2x+1 and y=x-2?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 2x+3y= -12 and 2x-y = -4?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x - y = -6 and x + y = 2?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y = 4x + 4 and 3x + 2y = 12?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y = 5x - 7 and -4 + y = -1 ?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given x= y - 11 and x - 3y = 1 ?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x + 3y= -9 and -8x + y = 29?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given y=-x+6 and y=3/4x-1?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 7x+4y=26 and 3x-8y=-18?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 9x - 3y = 3 and -3x - 8y = 17?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 4y = 11 - 3x and 3x + 2y = -5?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x - 7y = -3 and 6x - 5y = -1?

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• How do you determine whether a linear system has one solution, many solutions, or no solution when given #y=5x + -1# and #y=2x+2#?

• How do you determine whether a linear system has one solution, many solutions, or no solution when given 10x - 9y = 46 and -2x + 3y = 10?

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• What is a linear system?

• What is a consistent linear system?

• What defines an inconsistent linear system? Can you solve an inconsistent linear system?

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• If a system of equations has linearly dependent equations and an equal number of equations and variables, does it have to be consistent?

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• What is the span of a matrix?

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• How do you determine the value(s) of k such that the system of linear equations has the indicated number of solutions: An infinite number of solutionsfor 4x + ky = 6 and kx +y = -3?

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• What are the solutions to #y = -2x + 2# and #2y = -4x +4#?

• How do determine if #2x+3y=6, 2x+3y=7# has no solution, one solution, or an Infinite number of solutions and find the solution?

• How do determine if #x+y=-2,y=x+2# has no solution, one solution, or an Infinite number of solutions and find the solution?

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• Question #53b61

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• Question #951e6

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• Amanda pays an one-time fee of $100 and a monthly fee of $10 to belong to a gym. Maria pays only a monthly fee of $20 to belong to her gym. How do you write a system of equations to represent this situation?

  How do you determine if a linear system is consistent or inconsistent?

  Definition: A system of linear equations is said to be consistent if it has either one solution or infinitely many solutions. A system of linear equations is said to be inconsistent if it has no solution. system can be recorded compactly in a rectangular array called a matrix.

  How do you know if a system is inconsistency or consistency?

  To see if the pair of linear equations is consistent or inconsistent, we try to gain values for x and y. If both x and y have the same value, the system is consistent. The system becomes inconsistent when there are no x and y values that satisfy both equations.

  How do you know if a linear equation is consistent?

  A system with exactly one solution is called a consistent system. To identify a system as consistent, inconsistent, or dependent, we can graph the two lines on the same graph and see if they intersect, are parallel, or are the same line.

  How do you know if the linear equation is consistent inconsistent and dependent?

  A system of equations is consistent if it has at least one solution. A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.