Question

Solve for (x, y, z), if there is a solution to the given system of linear equations:

Answer 1

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

$\left\{\begin{matrix}x - 3y - 2z = -3\\ 3x + 2y - z = 12\\ -x - y + 4z = 3\end{matrix}\right$

Let's add the first and third equation to eliminate x:

$-4y+2z=0$

Solving for z

$z=2y$

Now we multiply the third equation by 3 and sum it to the second

$\left\{\begin{matrix}3x + 2y - z = 12\\ -3x -3 y + 12z = 9\end{matrix}\right.$

$-y+11z=21$

We know that x=2y, so

$-y+11(2y)=21$

$-y+22y=21$

$y=1$

This gives us

$z=2(1)=2$

From the very first equation we solve for x

$x=-3+ 3y + 2z$

Replacing y=1, z=2, we get

$x=-3+ 3(1) + 2(2)$

$x=4$

The solution is

x=4, y=1, z=2