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From Point to Point

Age 14 to 16 Short Challenge Level:

$x\begin{pmatrix}2\\-3\end{pmatrix} +y\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix} -\begin{pmatrix}10\\66\end{pmatrix}=\begin{pmatrix}10\\-54\end{pmatrix}$

$2x+3y=10$
$-3x+2y=-54$

$6x+9y=30$
$-6x+4y=-108$

$13y=-78$
$y=-6$
$x=14$

$\begin{pmatrix}10\\66\end{pmatrix}+14\begin{pmatrix}2\\-3\end{pmatrix} -6\begin{pmatrix}3\\2\end{pmatrix}=\begin{pmatrix}20\\12\end{pmatrix}$
You can find more short problems, arranged by curriculum topic, in our short problems collection.