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6.11: XYZ Extras

Difficulty Level: At Grade Created by: CK-12
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Extras for Experts XYZ - Solve Systems of Equations

Solutions

  1. \begin{align*}x = 5, \ y = 4, \ z = 6\end{align*}
  2. \begin{align*}x = 5, \ y = 9, \ z = 6\end{align*}
  3. \begin{align*}x = 7, \ y = 6, \ z = 9\end{align*}
  4. \begin{align*}x = 8, \ y = 7, \ z = 6\end{align*}

Eric wrote these equations to represent pictures of scales with blocks. Figure out the value of each unknown.

\begin{align*}1. \quad y + y + z + z = 20 \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + x + y = 14 \qquad \quad \quad \ \ y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + x + y + z = 20 \qquad \ \ \ z = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

\begin{align*}2. \quad x + x + y + z = 25 \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + y + y = 23 \qquad \qquad \quad y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + y + z = 20 \qquad \qquad \quad z = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

\begin{align*}3. \quad x + y + z + z = 31 \qquad \quad \ x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + y + z = 22 \qquad \qquad \quad y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + z = 16 \qquad \qquad \qquad \ \ z = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

\begin{align*}4. \quad x + y + z = 21 \qquad \qquad \quad x = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ x + x + y + z = 29 \qquad \quad \ y = \underline{\;\;\;\;\;\;\;\;\;\;}\!\\ {\;} \quad \ y + y + z = 20 \qquad \qquad \quad z = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.7.11