Solve the system for z.

Question

2x - y + 2z = 11
x - 2y - 3z = -5
-3x + z = -3

Answer 1

- 3 x + z = - 3 Add 3 x to both sides

- 3 x + 3 x + z = - 3 + 3 x

z = 3 x - 3

x - 2 y - 3 z = - 5

x - 2 y - 3 * ( 3 x - 3
) = - 5

x - 2 y - 3 * 3 x - 3 * ( - 3 = - 5

x - 2 y - 9 x + 9 = - 5

- 8 x - 2 y + 9 = - 5 Add 8 x - 9 to both sides

- 8 x - 2 y + 9 + 8 x - 9 = - 5 + 8 x - 9

- 2 y = - 14 + 8 x Divide both sides by - 2

y = - 14 / - 2 + 8 x / - 2

y = 7 - 4 x

2 x - y + 2 z = 11

2 x - ( 7 - 4 x ) + 2 * ( 3 x - 3 ) = 11

2 x - 7 + 4 x + 6 x - 6 = 11

12 x - 13 = 11 Add 13 to both sides

12 x - 13 + 13 = 11 + 13

12 x = 24 Divide both sides by 12

x = 24 / 12

x = 2

y = 7 - 4 x

y = 7 - 4 * 2

y = 7 - 8

y = - 1

z = 3 x - 3

z = 3 * 2 - 3

z = 6 - 3

z = 3

Solution :

x = 2 , y = - 1 , z = 3

Answer 2

-x+3y-z+w=-2
X-y+3z-w=0
y-z+4w=7
4x-y+z=5

Answer 3

x=4
y=-1
z=3

Answer 4

Matrix mathematics capter

Answer 5

Solve by linear equation x+y=1,3y+3z=+3x=4