2.3.3 Solving Equations Using Substitution

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$\begin{array}{ccc}\hfill 5x-2y& \hfill =\hfill & 26\hfill \\ \hfill 5(y+4)-2y& \hfill =\hfill & 26\hfill \\ \hfill 5y+20-2y& \hfill =\hfill & 26\hfill \\ \hfill 3y+20& \hfill =\hfill & 26\hfill \\ \hfill 3y& \hfill =\hfill & 6\hfill \\ \hfill y& \hfill =\hfill & =2\hfill \end{array}$

$\begin{array}{c}\hfill \\ \hfill 2+4& \hfill =\hfill & x\hfill \\ \hfill 6& \hfill =\hfill & x\hfill \end{array}$

$\begin{array}{ccc}\hfill 5(6)-2(2)=26& \hfill \hfill & \hfill \\ \hfill 30-4\stackrel{?}{=}26& \hfill \hfill & \hfill 2+4\stackrel{?}{=}6\\ \hfill 26=26✓& \hfill \hfill & \hfill 6=6✓\end{array}$

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$\begin{array}{ccc}\hfill 2m-2p& \hfill =\hfill & -6\hfill \\ \hfill 2m-2(2m+10)& \hfill =\hfill & -6\hfill \\ \hfill 2m-4m-20& \hfill =\hfill & -6\hfill \\ \hfill -2m-20& \hfill =\hfill & -6\hfill \\ \hfill -2m& \hfill =\hfill & 14\hfill \\ \hfill m& \hfill =\hfill & -7\hfill \end{array}$

$\begin{array}{ccc}\hfill p& \hfill =\hfill & 2m+10\hfill \\ \hfill p& \hfill =\hfill & 2(-7)+10\hfill \\ \hfill p& \hfill =\hfill & -14+10\hfill \\ \hfill p& \hfill =\hfill & -4\hfill \end{array}$

$\begin{array}{ccc}\hfill 2(-7)-2(-4)=-6& \hfill \hfill & \hfill -4=2(-7)+10\\ \hfill -14+8\stackrel{?}{=}-6& \hfill \hfill & \hfill -4\stackrel{?}{=}(-14)+10\\ \hfill -6=-6✓& \hfill \hfill & \hfill -4=-4✓\end{array}$

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$\frac{3}{2}$

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$\begin{array}{ccc}\hfill 2d& \hfill =\hfill & 8f\hfill \\ \hfill d& \hfill =\hfill & 4f\hfill \end{array}$

$\begin{array}{ccc}\hfill 18-4f& \hfill =\hfill & 2d\hfill \\ \hfill 18-4f& \hfill =\hfill & 2(4f)\hfill \\ \hfill 18-4f& \hfill =\hfill & 8f\hfill \\ \hfill 18& \hfill =\hfill & 12f\hfill \\ \hfill \frac{18}{12}& \hfill =\hfill & f\hfill \\ \hfill \frac{3}{2}& \hfill =\hfill & f\hfill \end{array}$

$\begin{array}{ccc}\hfill 2d& \hfill =\hfill & 8(\frac{3}{2})\hfill \\ \hfill 2d& \hfill =\hfill & 12\hfill \\ \hfill d& \hfill =\hfill & 6\hfill \end{array}$

$\begin{array}{ccc}\hfill & \hfill \hfill & \hfill 18-4f=2d\\ \hfill 2d=8f& \hfill \hfill & \hfill 18-4(\frac{3}{2})=2(6)\\ \hfill 2(6)=8(\frac{3}{2})& \hfill \hfill & \hfill 18-(2)(3)=12\\ \hfill 12\stackrel{?}{=}(4)(3)& \hfill \hfill & \hfill 18-6=12\\ \hfill 12=12✓& \hfill \hfill & \hfill 12=12✓\end{array}$

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$\begin{array}{ccc}\hfill w+\frac{1}{7}z& \hfill =\hfill & 4\hfill \\ \hfill w+\frac{1}{7}(3w-2)& \hfill =\hfill & 4\hfill \\ \hfill 7w+3w-2& \hfill =\hfill & 28\hfill \\ \hfill 10w-2& \hfill =\hfill & 28\hfill \\ \hfill 10w& \hfill =\hfill & 30\hfill \\ \hfill w& \hfill =\hfill & 3\hfill \end{array}$

$\begin{array}{ccc}\hfill z& \hfill =\hfill & 3w-2\hfill \\ \hfill z& \hfill =\hfill & 3(3)-2\hfill \\ \hfill z& \hfill =\hfill & 9-2\hfill \\ \hfill z& \hfill =\hfill & 7\hfill \end{array}$

$\begin{array}{ccc}\hfill w+\frac{1}{7}z=4& \hfill \hfill & \hfill z=3w-2\\ \hfill 3+\frac{1}{7}(7)=4& \hfill \hfill & \hfill 7=3(3)-2\\ \hfill 3+1\stackrel{?}{=}1=4& \hfill \hfill & \hfill 7\stackrel{?}{=}1=9-2\\ \hfill 4=4✓& \hfill \hfill & \hfill 7=7✓\end{array}$