Simultaneous Equations 3X3
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The solutions to the \(3 \times 3\) systems of simultaneous equations:
\(x + y + z = 6\,\,\,\,\,\,\,\,\,\,2x + 3y + z = 13\,\,\,\,\,\,\,\,\,\,x + 2y - z = 5{\rm{ }}\)
\begin{aligned}
x+y+z&=6 \cdots \cdots (1)\\
2 x+3y+z&=13\cdots \cdot \cdot (2)\\
x+2y-z&=5\cdots \cdots (3)\\
(1)+(3) \qquad 2x+3y&=11 \cdots \cdot \cdot(4)\\
(2)+(3) \qquad 3x+5y&=18 \cdots \cdot \cdot (5)\\
(4) \times 3 \qquad\;\;\, 6x+9y&=33 \cdots \cdot \cdot (6)\\
(5) \times 2 \qquad\, 6x+10y&=36 \cdots \cdot \cdot (7)\\
(6)-(7) \qquad \quad \;\, -y&=-3 \rightarrow y=3\\
\text { In }(4) \qquad\quad 2x+9&=11 \;\rightarrow x=1\\
\text { In } (1)\quad \;\;\; 1+3+z&=6 \;\;\;\rightarrow z=2
\end{aligned}
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