I was trying to figure out the curve of intersection of these 
2 planes:
$$3x - y + z = 4 $$
$$ y + z = 2.$$

I realize it will be a straight and not curved, and feel like I should be able to do the math but I just can't arrive at the posted answer. I was confused how they parametrized this and would just like to see the work so I can have an ah-ha moment. 
correct answer is : 

$$C(t)= \,\langle 2t, -1+3t, 3-3t\rangle$$ $t $ includes all real numbers.

Thanks