Suppose the two intersecting planes in 3-space have equations $ax + by + cz + d = 0$ and $a'x + b'y + c'z + d' = 0$ respectively. Since these form a system of two equations in three variables, solving this system will yield a solution $(x,y,z) = (x_0, y_0, z_0) + (x_1, y_1, z_1)t$ with a free variable $t$, and hence a parametric equation for the line of intersection of the two planes.
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