Question

Systems with three variables. solve each system of equation.

-4x-6y+4z=-14
3x-2y-5z=-2
x-4y-z=-2

Answer 1

1) -4x - 6y + 4z = -14

x : - 4x + 4z = -14 + 6y

- 4x = -14 + 6y - 4z Divide both sides by -4

x = -3/2 y + z + 7/2

y : -4x - 6y + 4z = -14
-6y + 4z = -14 + 4x
-6y = -14 + 4x - 4z

y = -2/3 x + 2/3 z + 7/3
z : -4x - 6y + 4z = -14
-6y + 4z = -14 + 4z
4z = -14 + 4z + 6y

z = x + 3/2 y + -7/2

2) 3x-2y-5z=-2

x : 3x-2y-5z=-2
3x - 2y = -2 + 5z
3x = -2 + 5z+ 2y

x = -2/3 + 5/3z + 2/3 y

y : 3x-2y-5z=-2
-2y - 5z = -2 - 3x
-2y = -2 - 3x + 5z

y = 1 + 3/2 x + -5/2z

z : 3x-2y-5z=-2
-2y - 5z = -2 - 3x
-5z = -2 - 3x - 2y

z = 3/5x + -2/5y + 2/5

3) x- 4y -z=-2

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

x = -2 + 4y +z

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

y = 1/4 x + 1/2 + -1/4 z

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

z = 2 + x - 4y