Question

X+2y-z=0 ,3x+2y+z=14,4x-2y+3z=11

Answer 1

Step-by-step explanation:

// Solve equation [2] for the variable z

[2] z = -3x - 2y + 14

// Plug this in for variable z in equation [1]

[1] x + 2y - (-3x-2y+14) = 0

[1] 4x + 4y = 14

// Plug this in for variable z in equation [3]

[3] 4x - 2y + 3•(-3x-2y+14) = 11

[3] -5x - 8y = -31

// Solve equation [1] for the variable y

[1] 4y = -4x + 14

[1] y = -x + 7/2

// Plug this in for variable y in equation [3]

[3] -5x - 8•(-x +7/2) = -31

[3] 3x = -3

// Solve equation [3] for the variable x

[3] 3x = - 3

[3] x = - 1

// By now we know this much :

x = -1

y = -x+7/2

z = -3x-2y+14

// Use the x value to solve for y

y = -(-1)+7/2 = 9/2

// Use the x and y values to solve for z

z = -3(-1)-2(9/2)+14 = 8

Solution :

{x,y,z} = {-1,9/2,8}