Question

Find the line of intersection of the planes
3x + 4y - z = 2 and x + y + z = 3?

Answer 1

can pick two points and project it?

Answer 2

Combine the two using substitution just as you would as if you were solving a system of equations. Out will pop the equation of a line. Let us try adding the two equations together for starters.\[\begin{array}{cr}&3x+4y-z=2\\+&x+y+z=3\\\hline &4x+5y=5\end{array}\]This will be the projection of the intersection line on the \(xy\)-plane. Solving for \(y\) gives us \(y=1-\frac{4}{5}x\). Perform a similar process to eliminate \(x\) from the two equations to solve for \(y\) in terms of z, say \(y=f(z)\). The the equation of the line will be given by the equations \(\boxed{1-\frac{4}{5}x=y=f(z)}\).

Answer 3

so if I had another problem where two z's don't cancel out so nicely, can I just pick any number I want?