Question
Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&-~~~~~ y&-~~~~~ z&~=~0\\2~ x&+~~~~ y&&~=~7\\-1~ x&&+~~5~ z&~=~9\end{array}$$
Answer
The solutions are:
$$ x = \dfrac{ 22 }{ 7 } ~,~y = \dfrac{ 5 }{ 7 } ~,~z = \dfrac{ 17 }{ 7 } $$Explanation
Step 1: Convert all decimals to fractions
$$\begin{array}{ cccc }~~ x&-~~~~~ y&-~~~~~ z&~=~0\\2~ x&+~~~~ y&&~=~7\\-1~ x&&+~~5~ z&~=~9\end{array}$$Step 2: Solve for $ z $.
$$ \begin{aligned} 5 ~ z & = 9 \\ z & = \dfrac{ 9 }{ 5 } \end{aligned} $$Step 3: Solve for $ y $ using the second equation:
$$ \begin{aligned}y &= 7\\y &= 7\\y &= 7 \end{aligned}$$Step 4: Solve for $ x $ by substituting $ y = 7 $ and $ z = \dfrac{ 9 }{ 5 } $ into the first equation.
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