The solution to the given system of equations is:
[tex](x, y, z) = \left(-\frac{87 + 111z}{11}, -\frac{15z + 18}{11}, z\right)[/tex]
There are infinite solutions for the system in the above format, you can choose the value of z and from this value find values for x and y.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
Applying the multiplication of the matrices, the equations are given as follows:
From the first equation, we have that:
2x = -6 - 6y - 12z
x = -3 - 3y - 6z
Replacing in the second equation, we have that:
-3 - 3y - 6z + 3y + 6z = -3
0z = 0
z = any value.
Hence we write the solutions as function of z.
Replacing in the third equation, we have that:
3x - 2y + 3z = 8.
3(-3 -3y - 6z) - 2y + 3z = 8
-9 - 9y - 18z - 2y + 3z = 9
-11y - 15z = 18
11y = -15z - 18.
[tex]y = \frac{-15z - 18}{11}[/tex]
The solution for x is:
x = -3 - 3y - 6z
[tex]x = -3 - \frac{45z + 54}{11} - 6z[/tex]
[tex]x = \frac{-33 - 45z - 54 - 66z}{11}[/tex]
[tex]x = -\frac{87 + 111z}{11}[/tex]
The solution for the system is:
[tex](x, y, z) = \left(-\frac{87 + 111z}{11}, -\frac{15z + 18}{11}, z\right)[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
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