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Richard Gudoski
Linear Systems in 3 Variables (Level 1)
May 26, 1:41:51 AM
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Solve the following system of equations for all three variables.
\[
\begin{aligned}
-2 x+3 y-4 z & =8 \\
5 x-3 y+5 z & =-8 \\
7 x-3 y+3 z & =8
\end{aligned}
\]
\[
x=
\]
$y=$
$z=$
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Answer

$\boxed{x = 2, y = -4, z = -6}$

Steps

Step 1 ：First, we use Gaussian elimination method to solve the system of linear equations with three variables x, y, and z.

Step 2 ：After solving the system, we get the final answer: $x = 2$, $y = -4$, and $z = -6$.

Step 3 ：$\boxed{x = 2, y = -4, z = -6}$