Show that each one of the following systems of equations is inconsistent.
x + y – 2z = 5;

x – 2y + z = - 2;

- 2x + y + z = 4.

Question

Show that each one of the following systems of equations is inconsistent.4x – 2y = 3;6x – 3y = 5.

Philoid · Accepted Answer

To prove: Set of given lines are inconsistent.

Given set of lines are : -

4x – 2y = 3

6x – 3y = 5

Converting the following equations in matrix form,

AX = B

4R₂ – 6R₁

Again converting into equation form, we get

4x – 2y = 3

0x + 0y = 2

∴ 0 = 2

which is not true

∴ 4x – 2y = 3

6x – 3y = 5 are inconsistent.

Show that each one of the following systems of equations is inconsistent.
4x – 2y = 3;

6x – 3y = 5.