solve for x, y, z, x-y-z=0 2x-3y+2z=7 -x+2y+z=1

Question

solve for x y z, x-y-z=0 ,2x-3y+2z=7 and -x+2y+z=1

Answer 1

x-y-z = 0 -----------> (1)

2x-3y+2z = 7-----------> (2)

-x+2y+z = 1 ----------> (3)

add the equations (1)and (3)

  x-y-z = 0

-x+2y+z = 1

___________

y = 1

Substitute the y value in equation (1).

x-1-z = 0

x-z =1-------> (4)

Substitute the y value in equation (3)

-x+2+z = 1

-x+z = -1

Multiple to each side by negitive one.

x-z = 1 ---------> (5)

Observe the equations (4) and (5) are parallel.

parallel lines are does not intersect.

So the given system has no solution.