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Solve the system of equations.

[tex]\[
\begin{array}{l}
6.3x - 1.5y + 1.3z = 10.77 \\
3.5x + 3.0y - 0.1z = -3.52 \\
2.8x - 4.5y + 2.6z = 17.53
\end{array}
\][/tex]

Select the correct choice below, and if necessary, fill in any answer boxes to complete your choice.

A. There is one solution. The solution set is [tex]\(\{(0.2561, -1.1989, 8.1974)\}\)[/tex]. [tex]\(\square\)[/tex]

B. The equations are dependent. The solution set is [tex]\(\{(x, y, z) \mid 3.5x + 3.0y - 0.1z = -3.52\}\)[/tex].

C. The system is inconsistent. The solution set is [tex]\(\varnothing\)[/tex].

Sagot :

GinnyAnsweridn
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.
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