Find the ordered pair (s, t) that satisfies the system
(s/2) + 5t =3 - 7t + 8s
3t - 6s = 9 - 2t
I defintely didn't do this in a smart way, but a more complicated manner.
First, let's put s in terms of t so we can do some subsitutions. We get
\(s=-\frac{2\left(-4t+1\right)}{5}\) from the first equation.
Subsituting this value of s into the second equation, we get
\(3t-6\left(-\frac{2\left(-4t+1\right)}{5}\right)=9-2t\)
Now, we solve for t. We get
\(\frac{-23t+12}{5}=9\\-23t+12=45\\t=-\frac{33}{23}\)
Now, we subsitute t back into the first equation to find s. We get
\(s=-\frac{62}{23}\)
Thus, we finally find the ordered pair as
\(s=-\frac{62}{23},\:t=-\frac{33}{23}\)
So our final answer is \((-62/23, -33/23)\)
Thanks! :)