Question

Consider the following system of equations: 1. X+Y-Z=1 2. 2X-5Y+Z=-1 3.7X-7Y-Z=k Determine the value(s) of k for which the solution to this system is line.

Answer 1

how will i know if the intersection of planes is a plane, a line, a point or no intersection using system of equations?

Answer 2

by solving system...if you assign k = 1 you get a situation where there are infinite solutions thus solution is a line

Add #1 and #2 --> 3x-4y = 0
Add #2 and #3 --> 9x -12y = k-1

if k=1 , infinite solutions
if k not equal 1, no solution

Answer 3

thanks a lot:))

Answer 4

yw