what is the solution to the system of equations

Question

3x-y+z=6

-3x-y+3z=0

x -3z=3

Answer 1

3x-y+z = 6 ---------> (1)

-3x-y+3z = 0 ---------> (2)

x-3z = 3 -----------> (3)

To eliminate the x,z add the equations (1),(2)

3x-y+z = 6

-3x-y+3z = 0

____________

4z = 6

Divide to each side by 4

4z/4 = 6/4

z = 3/2

Substitute the z value in equation (3).

x-3*3/2 = 3

x-9/2 = 3

Add 9/2 to each side

x-9/2+9/2 = 3+9/2

x = 15/2

Substitute the x,z in (1).

45/2-y+3/2 = 6

-y+24 = 6

Subtract 24 to each side

-y+24-24 = -24+6

-y = -18

Cancell the signs.

y = 18

Solution of given system x =15/2, y = 18, z = 3/2