To solve the given system of linear equations:
[tex]\[
\begin{array}{rcl}
6.3x - 1.5y + 1.3z &=& 10.77 \\
3.5x + 3.0y - 0.1z &=& -3.52 \\
2.8x - 4.5y + 2.6z &=& 17.53
\end{array}
\][/tex]
We solve for [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex].
The solution to this system of equations is:
[tex]\[ x = 0.7, \][/tex]
[tex]\[ y = -1.9, \][/tex]
[tex]\[ z = 2.7. \][/tex]
Therefore, the correct choice is:
A. There is one solution. The solution set is [tex]\(\{(0.7, -1.9, 2.7)\}\)[/tex].
Hence,
[tex]\[ \boxed{0.7} \][/tex]
[tex]\[ \boxed{-1.9} \][/tex]
[tex]\[ \boxed{2.7} \][/tex]
These values satisfy all three equations, indicating that there is indeed exactly one solution.
