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.


1