<s>[INST] Find parallel line value I've an homework problem that i'm unable to find the right answer.
The problem is:
The line $tx + sy = 2$ goes through point $(2,1)$ and is parallel to line $y = 8 -3x$, find the value of $t^2 + s^2$. 
$ A. {32\over49}$ $B.{18\over49}$ $C.{36\over49}$ $D.{25\over49} $ $E.{40\over49} $
I was able to find a parallel line at $ y = -3x + 7 $ but i'm unable to find any of the possible answers to be right.
 [/INST] Rewrite $y = -3x + 7$ in the form $tx + sy = 2$: $$\begin{align*}y & = -3x + 7 \\ 3x + y & = 7 \\ \frac{6}{7} x + \frac{2}{7} y & = 2.\end{align*}$$ By comparison of the form of $\frac{6}{7} x + \frac{2}{7} y = 2$ to that of $tx + sy = 2$, we find $t = \frac{6}{7}$ and $s = \frac{2}{7}$. Therefore, $$t^2 + s^2 = {\left(\frac{6}{7}\right)}^2 + {\left(\frac{2}{7}\right)}^2 = \frac{40}{49}.$$
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