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- A consistent system is considered to be a dependent system if the equations have the same slope and the same y -intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Solution: To check the condition of consistency we need to find out the ratios of the coefficients of the given equations, \ (\begin {array} {l}\frac {a_1} {a_2} = \frac {1} {2}\end {array} \) \ (\begin {array} {l}\frac {b_1} {b_2} = \frac {1} {2}\end {array} \) \ (\begin {array} {l}\frac {c_1} {c_2} = \frac {1} {2}\end {array} \)
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Sep 5, 2016 · Determine Whether a System of Equations is Consistent. This is very simple. This requires two steps. Convert to Row-Eschilon Form. Check if the last column is a pivot column. If it is, it's inconsistent. If it isn't, it's consistent . Brief Explanation
One of the easiest ways to find solutions of systems of linear equations (or show no solutions exist) is Gauss (or Gauss-Jordan) Row Reduction; it amounts to doing the kind of things you did, but in a systematic, algorithmic, recipe-like manner.
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A linear system is consistent if and only if its coefficient matrix has the same rank as does its augmented matrix (the coefficient matrix with an extra column added, that column being the column vector of constants).
Apr 21, 2015 · How do you tell if a system is consistent or inconsistent #2x + y = 7# and #x - 2y = 7#? 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?
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Definition. A system of equations is called inconsistent if it has no solutions. It is called consistent otherwise. A solution of a system of equations in n variables is a list of n numbers. For example, ( x , y , z )= ( 1, − 2,3 ) is a solution of (1.1.1).
