### Instruction: What is the ordered pair of integers $(x,y)$ for which $12x + 21y = 15$ and $21x + 12y = 51$?### Response: Let's solve this by the elimination method.
How do we do that?
We can multiply the first equation by 12, and the second equation by 21.
That gives us $144x + 252y = 180$ and $441x + 252y = 1071$.
Now we can subtract the first equation from the second equation.
That leaves us with $297x = 891$.
Now we can divide both sides of the equation by 297, which gives us $x = 3$.
Now we can substitute 3 for x in the first equation.
That gives us $12(3) + 21y = 15$.
Which simplifies to $36 + 21y = 15$.
And $21y = -21$.
So $y = -1$.