What values of x, y and z satisfy the following system of linear equations?
2004
What values of x, y and z satisfy the following system of linear equations?
- A.
x = 6, y = 3, z = 2
- B.
x = 12, y = 3, z = -4
- C.
x = 6, y = 6, z = -4
- D.
x = 12, y = -3, z = 0
Attempted by 3 students.
Show answer & explanation
Correct answer: C
The system is: x + 2y + 3z = 6, x + 3y + 4z = 8, and 2x + 2y + 3z = 12. Subtract the first equation from the second to get y + z = 2. Subtract twice the first equation from the third equation to get -2y - 3z = 0, or 2y + 3z = 0. Solving y + z = 2 and 2y + 3z = 0 gives z = -4 and y = 6. Substituting in the first equation gives x + 12 - 12 = 6, so x = 6. Therefore, x = 6, y = 6, z = -4.