# Equation of a Plane

## Homework Statement

Hello i just had a quick question, I am asked to Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x - axis.

## The Attempt at a Solution

Now i no if it gave you a point say A(3,4,5) i would use those as my x y and z values to solve for K in the equation 4x-3y-z-1+K(2x+4y+z-5)=0 and therefore finding the equation of the plane, but since it doenst give me a point and just a bit of information saying that it is parralel to the x axis, would i just use the elimation method to find the parametric equations for x y and z and then with that equation solve for the parameter lets say (t) and then therefore find points x,y,z and use those to solve for K?

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It is giving you one direction vector <1,0,0>

and you need second direction vector which you can find by finding the line equation at which two planes intersect.
(I am not sure how to find line equation of the intersection -
but I think converting both planes to vector form and making r1 = r2 would solve the problem.
There might be easier way)

HallsofIvy