Answer:
{x,y,z} = {0,13,20}
Step-by-step explanation:
x + y - z = -7
[2] 2x - y + z = 7
[3] x - 4y + 3z = 8
Solve by Substitution :
// Solve equation [3] for the variable x
[3] x = 4y - 3z + 8
// Plug this in for variable x in equation [1]
[1] (4y-3z+8) + y - z = -7
[1] 5y - 4z = -15
// Plug this in for variable x in equation [2]
[2] 2•(4y-3z+8) - y + z = 7
[2] 7y - 5z = -9
// Solve equation [2] for the variable y
[2] 7y = 5z - 9
[2] y = 5z/7 - 9/7
// Plug this in for variable y in equation [1]
[1] 5•(5z/7-9/7) - 4z = -15
[1] - 3z/7 = -60/7
[1] - 3z = -60
// Solve equation [1] for the variable z
[1] 3z = 60
[1] z = 20
// By now we know this much :
x = 4y-3z+8
y = 5z/7-9/7
z = 20
// Use the z value to solve for y
y = (5/7)(20)-9/7 = 13
// Use the y and z values to solve for x
x = 4(13)-3(20)+8 = 0
Solution :
{x,y,z} = {0,13,20}
