Find the line of intersection of the planes 𝑥+𝑦−2𝑧=2 and 2𝑥−𝑦+𝑧=1.

Answer 1

From the first equation we obtain: y=2z-x+2 and from the second equation we obtain: y=2x+z-1. Thus, we have the equality 2z-x+2=2x+z-1 or z=3x-3 and y=2x+3x-3-1=5x-4. Therefore, the equation of the line will be

x=t, y=5t-4 and z=3t-3 where t is in R.