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subject: Inconsistent System [print this page]

A system of linear equations is called an inconsistent system when there is no solution for the system.

There are 3 different types of solutions for system of equations as follows,

One solution

If the system of equations intersects each other at a single point, then this kind of system is said to be one solution system of equation.

Infinite number of solution:

If the system of equation coincides with each other then all points online will be the solution for the system of equation.

No solution or inconsistent:

If the system of equation is parallel then the system of equation is called as inconsistent system.

Sample Problems on Inconsistent System

Ex:1 Solve the following system of equation and find whether they are inconsistent or not.

4y - 5x = 7

8y - 10x = 28

Sol:-

4y - 5x = 7 ~~~~~~~~~ Equation 1.

8y - 10x = 28 ~~~~~~~~~ Equation 2.

Step:-1

Multiply equation 1 by 2

We get

2* (4y 5x = 7 )

8y 10 x = 14. ~~~~~~~~~ Equation 3

Now subtraction equation 2 and 3

We get

8y 10x = 28. ~~~~~~~ Equation 2

8y 10 x = 14. ~~~~~~~ Equation 3

_____________

0y + 0x = 14.

Here the solution for the system cant be determined because the two lines are parallel.

And this system of equations is an inconsistent system.

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Ex:2 Solve the following system of equation and find whether they are inconsistent or not.

2y - 4x = 24.

5y - 4x = 8.

Sol:-

2y - 4x = 24. ~~~~~~~~ Equation 1.

5y - 2x = 8. ~~~~~~~~ Equation 2.

Step:-1

Multiply equation 2 by 2

We get

2* (5y - 2x = 8 )

10y 4 x = 16. ~~~~~~~~~ Equation 3

Now subtraction equation 1 and 3

We get

2y 4x = 24. ~~~~~~~ Equation 2

10y 4 x = 16.. ~~~~~~~ Equation 3

_____________

-8y + 0x = 8

Now divide it by -8 on both side we get y = -1.

By plugging in the value of y in the System of equation 1, we get x = -13/2

Here the solution for the system of equation is 1, -13/2. And this system is not an inconsistent system.

This kind of system of equation is known as one solution system.

Exercise Problems:

1) Determine whether the system of equation is inconsistent or not

2 x + 3 y = 5.

6 x + 12 y = 45.

Answer:-This is not an inconsistent system.

2)Determine whether the system of equation is inconsistent or not

3 x + 3 y = 0.

5 x + 5 y = 4.

Answer:-This is an inconsistent system.

by: nitinp

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