Question

Solve.
-2x+3y-z = -2
3x+y=4
-2y + 2z = 4

Answer 1

(x,y,z) = (1,1,4)

Explanation:

`A: -2x + 3y - z = -2\\B: 3x+y=4\\C: -2y+2z=4\\`

`Solve\ B\ for\ y: y = 4-3x\\Solve\ C\ for\ z: 2z=4+2y\ \ z=2+y\\Substitute\ B_y\ into\ C_z: z = 2+4-3x\ \ z=6-3x\\Substitute\ B_(y\ in\ terms\ of\ x)\ and C_(z\ in\ terms\ of\ x) into A: \\-2x + 3(4-3x) - (6-3x) = -2\\Distribute: -2x + 12-9x-6+3x=-2\\Combine\ Like\ Terms\ on\ either\ side: -2x-9x+3x=-2-12+6\\Factor\ out\ x\ and\ perform\ arithmetic\ on\ right: x(-2-9+3) = -8\\Perform\ Arithmetic: x(-8)=-8\\Divide:x=1`

`Plug\ x\ into\ B_y: y=4-3(1)\\Perform\ Arithmetic: y=1\\Plug\ y\ into\ C_z: z=2+2(1)\\Perform\ Arithmetic: z=4`