Question

X+y-z=4, x-2y+3z=-6, 2x+3y+z=7

Answer 1

Answer:

{x,y,z} = {1,2,-1}

Step-by-step explanation:

x + y - z = 4 --------->1

x - 2y + 3z = -6 -------------->2 2x + 3y + z = 7----------------->3

Solve equation [3] for the variable z

z = -2x - 3y + 7

Plug this in for variable z in equation [1]

[1] x + y - (-2x-3y+7) = 4

[1] 3x + 4y = 11

Plug this in for variable z in equation [2]

[2] x - 2y + 3•(-2x-3y+7) = -6

[2] -5x - 11y = -27

Solve equation [1] for the variable y

[1] 4y = -3x + 11

[1] y = -3x/4 + 11/4

Plug this in for variable y in equation [2]

[2] -5x - 11•(-3x/4+11/4) = -27

[2] 13x/4 = 13/4

[2] 13x = 13

Solve equation [2] for the variable x

[2] 13x = 13

[2] x = 1

x = 1

y = -3x/4+11/4

z = -2x-3y+7

Use the x value to solve for y

y = -(3/4)(1)+11/4 = 2

Use the x and y values to solve for z

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

{x,y,z} = {1,2,-1}