Answer:
( choice B ) { x , y , z } = { -8 , 10 , -6 }
Step-by-step explanation:
* System of Linear Equations entered :
[1] 2x + 4y + 3z = 6
[2] 5x + 8y + 6z = 4
[3] 4x + 5y + 2z = 6
* Solve by Substitution :
// Solve equation [3] for the variable z
[3] 2z = -4x - 5y + 6
[3] z = -2x - 5y/2 + 3
// Plug this in for variable z in equation [1]
[1] 2x + 4y + 3•(-2x-5y/2+3) = 6
[1] -4x - 7y/2 = -3
[1] -8x - 7y = -6
// Plug this in for variable z in equation [2]
[2] 5x + 8y + 6•(-2x-5y/2+3) = 4
[2] -7x - 7y = -14
// Solve equation [2] for the variable y
[2] 7y = -7x + 14
[2] y = -x + 2
// Plug this in for variable y in equation [1]
[1] -8x - 7•(-x +2) = -6
[1] -x = 8
// Solve equation [1] for the variable x
[1] x = - 8
// By now we know this much :
x = -8
y = -x+2
z = -2x-5y/2+3
// Use the x value to solve for y
y = -(-8)+2 = 10
// Use the x and y values to solve for z
z = -2(-8)-(5/2)(10)+3 = -6
