What is the point of intersection of L and P?

Explanation

To find points on L, we add the two plane equations defining it: (x+y+z+4) + (2x-y-z+8) = 0 \implies 3x+12=0 \implies x=-4. Substituting x=-4 into x+y+z+4=0 gives -4+y+z+4=0 \implies z=-y. Now substitute x=-4 and z=-y into the plane P: x+2y+3z+1=0 \implies -4+2y+3(-y)+1=0 \implies -3-y=0 \implies y=-3. This means z=-(-3)=3. The point of intersection is (-4, -3, 3).

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