Answer:
(2,-6,1)
Step-by-step explanation:
y = -2x + z - 3
5x - 2•(-2x+z -3) + 2z = 24
9x = 18
9x = 18
x = 2
3•(2) - z = 5
- z = -1
z = 1
x = 2
y = -2x+z-3
z = 1
y = -2(2)+(1)-3 = -6
{x,y,z} = {2,-6,1}
Answer: The correct option is
(D) (2, -6, 1).
Step-by-step explanation: We are given to solve the following system of linear equations :
[tex]2x+y-z=-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x-2y+2z=24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x-z=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
From equation (iii), we have
[tex]3x-z=5\\\\\Rightarrow z=3x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
Substituting the value of z from equation (iv) in equations (i) and (ii), we have
[tex]2x+y-(3x-5)=-3\\\\\Rightarrow -x+y+5=-3\\\\\Rightarrow x-y=8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)[/tex]
and
[tex]5x-2y+2(3x-5)=24\\\\\Rightarrow 11x-2y=34~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(vi)[/tex]
(v) × 2 - (vi) gives us
[tex]2(x-y)-(11x-2y)=16-34\\\\\Rightarrow -9x=-18\\\\\Rightarrow x=2.[/tex]
So, from equation (v), we get
[tex]2-y=8\\\\\Rightarrow y=2-8\\\\\Rightarrow y=-6.[/tex]
From (iv), we get
[tex]3\times 2-5=z\\\\\Rightarrow z=1.[/tex]
Thus, the required solution is
(x, y, z) = (2, -6, 1).
Option (D) is CORRECT.
