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

(s/2) + 5t =3 - 7t + 8s

3t - 6s = 9 - 2t

eramsby1O1O Jun 15, 2024

#1**+1 **

First, let's put s in terms of t so we can do some subsitutions. We get

\(\quad s=-\frac{2\left(-4t+1\right)}{5}\) 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

\(s=-\frac{62}{23}\)

We get \(s=-\frac{62}{23},\:t=-\frac{33}{23}\)

So our final answer is \((-62/23, -33/23)\)

Thanks! :)

NotThatSmart Jun 16, 2024

#1**+1 **

Best Answer

First, let's put s in terms of t so we can do some subsitutions. We get

\(\quad s=-\frac{2\left(-4t+1\right)}{5}\) 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

\(s=-\frac{62}{23}\)

We get \(s=-\frac{62}{23},\:t=-\frac{33}{23}\)

So our final answer is \((-62/23, -33/23)\)

Thanks! :)

NotThatSmart Jun 16, 2024