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

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

3t - 6s = 9 - 2t

Rangcr897 Jul 30, 2024

#1**+1 **

First, let's simplify both equations to setup an interesting way to solve the problem.

\((s/2) + 5t = 3 - 7t + 8s → s + 10t = 6 - 14t + 16s → -15s + 24t = 6 \space\space\space \text{(1st equation)} \\ 3t - 6s = 9 -2t → 6s + 5t = 9 \space\space\space \text{(2nd equation)} \)

Now, let's mulitply the 1st equation by 6 and the 2nd equation by 15

These numbers seem random, we when we write it out, we can see why it's so important. We get

\(-90s + 144t = 36 \\ 90s + 75t = 135 \)

Now we have the opposite s coefficients. Adding these equations, we get

\(219 t = 171 \)

\(t = 171 / 219 = 57 / 73 \)

Now, we can find s through the value of t. We get

\(6s + 5(57/73) = 9 \\ 6s + 285/73 = 9 \\ 6s = 9 - 285/73 \\ 6s = 372/73 \\ s = 62 / 73\)

Thus, our ordered pair (s, t) is \((57/73, 62/73)\)

Thanks! :)

NotThatSmart Jul 30, 2024