### Instruction: At which point do the lines $s=9-2t$ and $t=3s+1$ intersect? Give your answer as an ordered pair in the form $(s, t).$.### Response: To find the point of intersection, I need to find the values of $s$ and $t$ that satisfy both equations simultaneously.
One way to do that is to substitute one equation into the other and solve for one variable.
Since the first equation is already solved for $s$, I can plug that into the second equation and get: $t=3(9-2t)+1$.
Now I have a single equation in one variable that I can simplify and solve: $t=27-6t+1$, $7t=28$, $t=4$.
Now that I have $t$, I can plug it back into either equation to find $s$. I'll use the first one: $s=9-2(4)$, $s=1$.
Therefore, the point of intersection is $(1, 4)$.