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# 6.11: XYZ Extras

Difficulty Level: At Grade Created by: CK-12

Extras for Experts XYZ - Solve Systems of Equations

Solutions

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

1.y+y+z+z=20x= x+x+y=14  y= x+x+y+z=20   z=\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*}

2.x+x+y+z=25x= x+y+y=23y= x+y+z=20z=\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*}

3.x+y+z+z=31 x= x+y+z=22y= x+z=16  z=\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*}

4.x+y+z=21x= x+x+y+z=29 y= y+y+z=20z=\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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Date Created:
Feb 23, 2012