9438
/www/nrich/html/content/id/9438/
1
2012-09-18T14:43:39
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How can you get from $(10,66)$ to $(20,12)$<br></br>
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using only integer multiples of the vectors<br></br>
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$\begin{pmatrix}2\\-3\end{pmatrix}$ and $\begin{pmatrix}3\\2\end{pmatrix}$?<br></br>
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If you liked this problem, <a href="/7453">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</mdoxml>
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$x\begin{pmatrix}2\\-3\end{pmatrix} +y\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix} -\begin{pmatrix}10\\66\end{pmatrix}=\begin{pmatrix}10\\-54\end{pmatrix}$<br></br>
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$2x+3y=10$<br></br>
$-3x+2y=-54$<br></br>
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$6x+9y=30$<br></br>
$-6x+4y=-108$<br></br>
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$13y=-78$<br></br>
$y=-6$<br></br>
$x=14$<br></br>
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$\begin{pmatrix}10\\66\end{pmatrix}+14\begin{pmatrix}2\\-3\end{pmatrix} -6\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix}$</mdoxml>
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Vectors - Short Problem
Can you combine vectors to get from one point to another?
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DisplayCabinet
Secondary Mapping Document
Vectors US