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

$\begin{array}{rl}2x_1+x_2-x_3& =1\\ x_1+x_2& =1.\end{array}$

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.