use Cramer's rule to solve this linear system.



Write it this way with 0 coefficients for the missing letters:



We begin by finding the determinant . It consists 
of just the three columns of x, y, and z coefficients,
in that order, but does not contain the constants, the
three numbers to the right of the equal signs.

.

It has value .

Next we find .

Dx has all the same elements as D except that the 1st column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

.

It has value .

Next we find .

Dy has all the same elements as D except that the 2nd column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

.

It has value .

Next we find .

Dz has all the same elements as D except that the 3rd column is replaced by
the three numbers that occur after the equal signs in the system, in the
order that they occur top to bottom:

..

It has value .

The values for x, y, and z are:



If you don't know how to find the value of a 3×3 determinant,
go here:

https://www.youtube.com/watch?v=V3e7m-qFDFU 

Edwin

In addition,  there are many free of charge SOLVERS on a Cramer's rule in the Internet.

One of such popular solvers is in this site under the links

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/determinant-of-3x3-matrix.solver

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver


Also, there are many sites in the Internet containing (free of charge) solvers to calculate 3x3 - determinants 
and to solve systems of equations by the Cramer's rule -- see, for example,

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/determinant-of-3x3-matrix.solver

and

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

directly in the site www.algebra.com

and universal multi-purpose solver 

    http://www.reshish.com

with many options.