Solve the following system of linear equations:
x + y + z = 15, 2x - y + z = 12 and x - y - z = -1
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. x = 7, y = 5, z = 3.
Given,
x + y + z = 15, ----- (1)
2x - y + z = 12 ----- (2)
x - y - z = -1 ---- (3)
From equation (3), we get
⇒ x = y + z - 1
Using the above equation in (1), we get
⇒ y + z - 1 + y + z = 15
⇒ y + z = 8 -------- (4)
Now using equation (4) in (1),
⇒ x = 15 - 8 = 7
Putting the value of x in equation (1) and (2) and solving them,
⇒ y + z = 8 and z - y = -2
⇒ y = 5 and z = 3
Hence, x = 7, y = 5, z = 3