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so i was stuck at a question and i dont know how to do it

6a + b = 16
5a - 2b = 19

 Jun 17, 2015

Best Answer 

 #1
avatar+20850 
+10

6a + b = 16
5a - 2b = 19

 

$$\small\text{$
\begin{array}{lrcl}
(1) & 6a + b &=& 16 \qquad | \qquad -6a\\
& \mathbf{b} &=& \mathbf{16 -6a} \\
\\
\hline
\\
(2) & 5a - 2b &=& 19 \qquad | \qquad \mathbf{b} = \mathbf{16 -6a}\\
& 5a -2(\mathbf{16 -6a}) &=& 19 \\
& 5a -32 + 12a &=& 19 \\
& 17a -32 &=& 19 \qquad | \qquad +32\\
& 17a &=& 19 +32\\
& 17a &=& 51 \qquad | \qquad :17\\
& a &=& \dfrac{51}{17} \\
& \mathbf{a} & \mathbf{=} & \mathbf{3} \\
\\
\hline
\\
& b &=& 16- 6a \qquad | \qquad \mathbf{a} = \mathbf{3} \\
& b &=& 16 - 6 \cdot \mathbf{3} \\
& b &=& 16 - 18 \\
& \mathbf{b} &\mathbf{=} & \mathbf{-2} \\
\\
\hline
\\
\end{array}
$}}$$

 

 Jun 17, 2015
 #1
avatar+20850 
+10
Best Answer

6a + b = 16
5a - 2b = 19

 

$$\small\text{$
\begin{array}{lrcl}
(1) & 6a + b &=& 16 \qquad | \qquad -6a\\
& \mathbf{b} &=& \mathbf{16 -6a} \\
\\
\hline
\\
(2) & 5a - 2b &=& 19 \qquad | \qquad \mathbf{b} = \mathbf{16 -6a}\\
& 5a -2(\mathbf{16 -6a}) &=& 19 \\
& 5a -32 + 12a &=& 19 \\
& 17a -32 &=& 19 \qquad | \qquad +32\\
& 17a &=& 19 +32\\
& 17a &=& 51 \qquad | \qquad :17\\
& a &=& \dfrac{51}{17} \\
& \mathbf{a} & \mathbf{=} & \mathbf{3} \\
\\
\hline
\\
& b &=& 16- 6a \qquad | \qquad \mathbf{a} = \mathbf{3} \\
& b &=& 16 - 6 \cdot \mathbf{3} \\
& b &=& 16 - 18 \\
& \mathbf{b} &\mathbf{=} & \mathbf{-2} \\
\\
\hline
\\
\end{array}
$}}$$

 

heureka Jun 17, 2015

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