The solution of system of equations - x - 5y - 5z = 2 and 4x - 5y + 4z = 19 and x + 5y - z = -20 are (x, y, z) = (-2, -3, 3).
Solution:
Given, system of equations are
-x – 5y – 5z = 2 ⇒ (1)
4x – 5y + 4z = 19 ⇒ (2)
X + 5y – z = -20 ⇒ (3)
We have to solve the given system of equations.
Now add (1) and (3)
(1) ⇒ -x – 5y – 5z = 2
(3) ⇒ x + 5y – z = -20
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(+) 0 + 0 – 6z = -18
6z = 18
z = 3. Now substitute z value in (3) and (2)
(3) ⇒ x + 5y – 3 = -20 ⇒ x + 5y = -17 ⇒ (4)
(2) ⇒ 4x – 5y + 4(3) = 19 ⇒ 4x – 5y = 7 ⇒ (5)
Now add (4) and (5)
(4) ⇒ x + 5y = -17
(5) ⇒ 4x – 5y = 7
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(+) 5x + 0 = -10 ⇒ 5x = -10 ⇒ x = -2, substitute x value in (4)
(4) ⇒ -2 + 5y = -17 ⇒ 5y = -15 ⇒ y = -3
Hence, the solution for given system of equations is (-2, -3, 3).