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.