Respuesta :
Answer:
{x,y,z}={5,−3,3}
Step-by-step explanation:
[1] 2x + 4y + z = 1
[2] x - 2y - 3z = 2
[3] x + y - z = -1
// Solve equation [3] for the variable y
[3] y = -x + z - 1
// Plug this in for variable y in equation [1]
[1] 2x + 4•(-x +z -1) + z = 1
[1] -2x + 5z = 5
// Plug this in for variable y in equation [2]
[2] x - 2•(-x +z -1) - 3z = 2
[2] 3x - 5z = 0
// Solve equation [2] for the variable x
[2] 3x = 5z
[2] x = 5z/3
// Plug this in for variable x in equation [1]
[1] -2•(5z/3) + 5z = 5
[1] 5z/3 = 5
[1] 5z = 15
// Solve equation [1] for the variable z
[1] 5z = 15
[1] z = 3
// By now we know this much :
x = 5z/3
y = -x+z-1
z = 3
// Use the z value to solve for x
x = (5/3)(3) = 5
// Use the x and z values to solve for y
y = -(5)+(3)-1 = -3
Solution :
{x,y,z} = {5,-3,3}
