Find the point of intersection of the line
\[\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}\]and $x - y + z = 5.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the point of intersection of the line
\[\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}\]and $x - y + z = 5.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(2,-1,2)
Find the point of intersection of the line
\[\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}\]and $x - y + z = 5.$
train