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Find the ordered pair $(s,t)$ that satisfies the system

\begin{align*}

  \dfrac{s}{2} + 5t &= 3,\\

  3t - 6s &= 9.

\end{ali

gn*}

 Jun 27, 2024
 #1
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\(\begin{align*} \dfrac{s}{2} + 5t &= 3,\\ 3t - 6s &= 9. \end{align*}\)

so ill first multiply the top equation by twelve to get 6s+60t=36

ill rearange the second equation to get -6s+3t=9

ill "add" the two equations to cancel out the s to get 63t=45

t=5/7

ill substitute t back into the first equation to get s/2+25/7=3

multiplying by two gets s+50/7=6

s=6-50/7

s=42/7-50/7

s=-8/7

so the ordered pair \((s,t)\)would be \(\boxed{(-\frac{8}{7},\frac{5}{7})}\)

 Jun 27, 2024

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