Solve the system.?

Question

x-2y-z=1 
-2x+4y+2z=-2 
-4x+8y+4z=-4

Answer 1

The system of equations are : x - 2y - z = 1         → ( 1 )

                                           - 2x + 4y + 2z = - 2 → ( 2 )

                                           - 4x + 8y + 4z = - 4 → ( 3 )

Multiply equation (1) by negative 1.

- x + 2y + z = - 1 → ( 4 )

Divide equation (2) by 2.

- x + 2y + z = - 1 → ( 5 )

Divide equation (3) by 4.

- x + 2y + z = - 1 → ( 6 )

Observe, equations (4), (5), and (6).

To solve for the values of x, y and z it is essential to have three different equations.

Since, the three equations given are exactly same, it can not be solved.

The equation is of a three dimensional system plane

So, there is no solution for the given system.