Answer:
x=4, y=1, z=2
Step-by-step explanation:
System Of 3 Linear Equations
When 3 variables x,y,z are related through 3 independent linear equations, we could find a combination of them which makes the 3 equations become identities. That can be achieved in a very high number of methods.
Let's solve the system of equations shown in the question
[tex]\left\{\begin{matrix}x - 3y - 2z = -3\\ 3x + 2y - z = 12\\ -x - y + 4z = 3\end{matrix}\right[/tex]
Let's add the first and third equation to eliminate x:
[tex]-4y+2z=0[/tex]
Solving for z
[tex]z=2y[/tex]
Now we multiply the third equation by 3 and sum it to the second
[tex]\left\{\begin{matrix}3x + 2y - z = 12\\ -3x -3 y + 12z = 9\end{matrix}\right.[/tex]
[tex]-y+11z=21[/tex]
We know that x=2y, so
[tex]-y+11(2y)=21[/tex]
[tex]-y+22y=21[/tex]
[tex]y=1[/tex]
This gives us
[tex]z=2(1)=2[/tex]
From the very first equation we solve for x
[tex]x=-3+ 3y + 2z[/tex]
Replacing y=1, z=2, we get
[tex]x=-3+ 3(1) + 2(2)[/tex]
[tex]x=4[/tex]
The solution is
x=4, y=1, z=2
