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# System

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Find the ordered pair, (s, t) that satisfies the system
(s/2) - 3t = -1,
3t - 2s = 3 + s - t

Apr 13, 2022

#1
+326
+1

$$\begin{bmatrix}\left(\frac{s}{2}\right)-3t=-1\\ 3t-2s=3+s-t\end{bmatrix}$$

$$\mathrm{Substitute\:}s=-2+6t$$

$$\begin{bmatrix}3t-2\left(-2+6t\right)=3-2+6t-t\end{bmatrix}$$

$$\begin{bmatrix}-9t+4=5t+1\end{bmatrix}$$

$$t=3/14$$

$$\mathrm{Substitute\:} t$$

$$s=-2+6\cdot \frac{3}{14}$$

$$s=-5/7$$

$$=$$$$(-5/7, 3/14)$$

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Apr 13, 2022

#1
+326
+1

$$\begin{bmatrix}\left(\frac{s}{2}\right)-3t=-1\\ 3t-2s=3+s-t\end{bmatrix}$$

$$\mathrm{Substitute\:}s=-2+6t$$

$$\begin{bmatrix}3t-2\left(-2+6t\right)=3-2+6t-t\end{bmatrix}$$

$$\begin{bmatrix}-9t+4=5t+1\end{bmatrix}$$

$$t=3/14$$

$$\mathrm{Substitute\:} t$$

$$s=-2+6\cdot \frac{3}{14}$$

$$s=-5/7$$

$$=$$$$(-5/7, 3/14)$$

Vinculum Apr 13, 2022