Introduction to inconsistent system of linear equation
In a system of linear equation, if there no one set of solution that can satisfy all the equations in the system then the system of linear equation are called inconsistent.
For example: 2x + y + 5 and 4x +2y = 7
Here if you try to solve these two equations, you will find that the variable get cancelled and become zero on the left side but then will be a consent on the right side. Here that is 0 = 3 which is not equal. Hence we cannot find a set of values to satisfy both the equations. Otherwise also, we can interpret this situation as they will be parallel lines, hence they won’t meet each other.
Now let us see few problems of this kind.
Example Problems on Inconsistent System of Linear Equation:
Ex 1: Check the following equations are consistent or inconsistent:
3x + 4y = 12 and 6x + 8y = 14.
Soln: Given lines are: 3x + 4y = 12 -------- 1
6x + 8y = 14 ----------2
(2)` xx ` (1)` implies` 6x + 8y = 24
(-)` xx` (2)` implies` 6x + 8y = 14` implies` 0 `!=` 10.
Since zero cannot be equal to 10, it is clear that the lines are inconsistent.
Ex 2: Check whether the following system of linear equations are consisted or inconsistent: x + y = 5, x – y = 3.
Soln: Given: x + y = 5 ---------------1
x – y = 3 -----------------2
Therefore (1 +2) `implies` 2x = 8 `implies` x = 4
Therefore ` implies` 4 + y = 5 `implies` y =1
Since there is a unique value for x and y, (1) and (2) are consistent. Looking out for more help on Algebra Word Problems in algebra by visiting listed websites.
More Example Problems on Inconsistent System of Linear Equation:
Ex 3: Check the consistency of the following equations:
` x/4` + `y/5 ` = 12 and `x/2` + `[2y]/5` = 24
Soln: Given: `x/4` + `y/5` = 12 ----------------(1)
`x/2` + `(2y)/5` = 24 ----------------(2)
Therefore (1) `xx` (2) `implies` `2(x/4)` + `2(y/5)` = 2`xx` 12
`implies`` x/2` +`[2y]/5` = 24 ------(3)
Since (2) amd (3) are same, (1) and (2) represents the same line. Therefore they are consistent and have infinitely many solutions.
In a system of linear equation, if there no one set of solution that can satisfy all the equations in the system then the system of linear equation are called inconsistent.
For example: 2x + y + 5 and 4x +2y = 7
Here if you try to solve these two equations, you will find that the variable get cancelled and become zero on the left side but then will be a consent on the right side. Here that is 0 = 3 which is not equal. Hence we cannot find a set of values to satisfy both the equations. Otherwise also, we can interpret this situation as they will be parallel lines, hence they won’t meet each other.
Now let us see few problems of this kind.
Example Problems on Inconsistent System of Linear Equation:
Ex 1: Check the following equations are consistent or inconsistent:
3x + 4y = 12 and 6x + 8y = 14.
Soln: Given lines are: 3x + 4y = 12 -------- 1
6x + 8y = 14 ----------2
(2)` xx ` (1)` implies` 6x + 8y = 24
(-)` xx` (2)` implies` 6x + 8y = 14` implies` 0 `!=` 10.
Since zero cannot be equal to 10, it is clear that the lines are inconsistent.
Ex 2: Check whether the following system of linear equations are consisted or inconsistent: x + y = 5, x – y = 3.
Soln: Given: x + y = 5 ---------------1
x – y = 3 -----------------2
Therefore (1 +2) `implies` 2x = 8 `implies` x = 4
Therefore ` implies` 4 + y = 5 `implies` y =1
Since there is a unique value for x and y, (1) and (2) are consistent. Looking out for more help on Algebra Word Problems in algebra by visiting listed websites.
More Example Problems on Inconsistent System of Linear Equation:
Ex 3: Check the consistency of the following equations:
` x/4` + `y/5 ` = 12 and `x/2` + `[2y]/5` = 24
Soln: Given: `x/4` + `y/5` = 12 ----------------(1)
`x/2` + `(2y)/5` = 24 ----------------(2)
Therefore (1) `xx` (2) `implies` `2(x/4)` + `2(y/5)` = 2`xx` 12
`implies`` x/2` +`[2y]/5` = 24 ------(3)
Since (2) amd (3) are same, (1) and (2) represents the same line. Therefore they are consistent and have infinitely many solutions.
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