x-y-2z=4, -x+2y+z=1 and -x+y-3z=11 by elimination?

Question

How do you solve this?

 

Answer 1

Elimination method

Given equations are x-y-2z = 4 ---> (1)

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

-x+y-3z = 11 ---> (3)

To eliminate the x value add (1)&(2).

x-y-2z = 4

-x+2y+z = 1

___________

y-z = 5 ---> (4)

To eliminate the x value add (1)&(3).

x-y-2z = 4

-x+y-3z = 11

___________

-5z = 15

Divide to each side by negitive 5.

-5z/-5 = 15/-5

z = -3

Substitute the z value in (4).

y+3 = 5

Subtract 3 from each side.

y+3-3 = 5-3

y = 2

Substitute the y, z value in (1).

x-2+6 = 4

x+4 = 4

Subtract 4 from each side.

x+4-4 = 4-4

x = 0

Solution x = 0, y = 2, z = -3.