Q2 of 98 Page 310

Show that each one of the following systems of equations is inconsistent.

2x + 3y = 5;


6x + 9y = 10.



To prove: Set of given lines are inconsistent.


Given set of lines are : -


2x + 3y = 5


6x + 9y = 10


Converting the following equations in matrix form,


AX = B



R2 – 3R1



Again converting into equation form, we get


2x + 3y = 5


0x + 0y = - 5


∴ 0 = - 5


which is not true


∴ 2x + 3y = 5


6x + 9y = 10 are inconsistent.


More from this chapter

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1

Show that each one of the following systems of equations is inconsistent.

x + 2y = 9;


2x + 4y = 7.


 3

Show that each one of the following systems of equations is inconsistent.

4x – 2y = 3;


6x – 3y = 5.


 4

Show that each one of the following systems of equations is inconsistent.

6x + 4y = 5;


9x + 6y = 8.


 5

Show that each one of the following systems of equations is inconsistent.

x + y – 2z = 5;


x – 2y + z = - 2;


- 2x + y + z = 4.