solve for x,y,z

Answer 1

-2x + y -z =-2

3x -y +z = 1

3x + 3y + z = -1

use substitution, elimination or matrix algebra

add the 1st & 2nd equations to get x =-1

then substitute that x value into the equations to reduce

it to 2 variables 2 equations which are more easily solved

to find y= -1/2 and z = 7/2 = 3 1/2

solution is (x,y,z) = (-1,-1/2, 7/2)

check the solution

-2(-1) +(-1/2) -(7/2) = -2

2 -1/2 -7/2 = -2

-8/2 = -2-2

-4 =-4

3(-1)-(-1/2) +(7/2) = 1

-3 +1/2 +7/2 = 1

-3+8/2 =1

-3+4 = 1

3(-1) +3(-1/2) + 7/2 = -1

-3 -3/2 +7/2 = -1

-3 +4/2 = -1

-3 +2 = -1

-1 = -1

it checks out for all 3 original equations

alternative method is use matrix (linear) algebra

and row operations

another strategy is graph the 3 equations

and see where they intersect

but 3 D graphs are difficult to do