Answer: {x,y,z}={-11/14,27/7,-41/14}
Explanation:
System of Linear Equations entered :
[1] x+y-z=6
[2] 2x-3y+2z=-19
[3] -x+4y-x=17
Equations Simplified or Rearranged :
[1] x + y - z = 6
[2] 2x - 3y + 2z = -19
[3] -2x + 4y = 17
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = -x + z + 6
// Plug this in for variable y in equation [2]
[2] 2x - 3•(-x +z +6) + 2z = -19
[2] 5x - z = -1
// Plug this in for variable y in equation [3]
[3] -2x + 4•(-x +? +6) = 17
[3] -6x = -7
// Solve equation [2] for the variable z
[2] z = 5x + 1
// Plug this in for variable z in equation [3]
[3] -6x = -7
[3] 14x = -11
// Solve equation [3] for the variable x
[3] 14x = - 11
[3] x = - 11/14
// By now we know this much :
x = -11/14
y = -x+z+6
z = 5x+1
// Use the x value to solve for z
z = 5(-11/14)+1 = -41/14
// Use the x and z values to solve for y
y = -(-11/14)+(-41/14)+6 = 27/7
Solution :
{x,y,z} = {-11/14,27/7,-41/14}