solve linear equation 6x-2y+2z=2, 4x+8y-2z=5, -2x-4y+z=-2

Question

Try to solve the system of equations and explain result.

Answer 1

Reduce the equations to their simplest form:

A: 2x-y+z=1

B: 2x+4y-z=2.5

C: -2x-4y+z=-2

D: A+B: 4x+3y=3.5

E: B+C: 0=0.5 which is false, so the equations are inconsistent. This means that there is no solution.

One of B or C would need to be chosen to be true, which would then provide two equations but three unknowns, and the best that could be achieved is some relation between the variables. For example, x and y could be both be expressed in terms of z.