Respuesta :
The point to the system of solution is (3, 3, –2).
Solution:
Given equations are
x – y – 2z = 4 – – – – (1)
–x + 3y – z = 8 – – – – (2)
–2x – y – 4z = –1 – – – – (3)
Let us first eliminate x from 2 equations.
Add (1) and (2)
x – y – 2z – x + 3y – z = 4 + 8
⇒ 2y – 3z = 12 – – – – (4)
Multiply equation (1) by 2 and add with equation (3)
2x – 2y – 4z – 2x – y – 4z = 8 – 1
⇒ –3y – 8z = 7 – – – – (5)
Now, Multiply equation (4) by 3 and equation (5) by 2 and add them.
6y – 9z – 6y – 16z = 36 + 14
⇒ –25z = 50
⇒ z = –2
Substitue z = –2 in equation (4), we get
⇒ 2y – 3(–2) = 12
⇒ 2y = 12 – 6
⇒ y = 3
Substitute, z = –2 and y = 3 in equation (1), we get
⇒ x – 3 – 2(–2) = 4
⇒ x – 3 + 4 = 4
⇒ x + 1 = 4
⇒ x = 3
Hence the point to the system of solution is (3, 3, –2).
