Science:Math Exam Resources/Courses/MATH152/April 2012/Question 01 (b)/Solution 1

From 1(a) we saw that the equations for the planes $S_{1}$ and $S_{2}$ are

${\begin{aligned}2x_{1}+x_{2}-x_{3}&=1\\x_{1}+x_{2}&=1.\end{aligned}}$

These two equations taken together are precisely the equation form of the line since any $x_{1},x_{2}$ and $x_{3}$ that satisfy this will be on both planes and therefore be on the line of intersection.