A system of equations is given as follows:
1. x+y+2z=1
2. kx+2y+4z=k

For what value of k does the system have an infinite number of solutions? Determine the solution to the system for this value of k.

Question

A system of equations is given as follows:
1. x+y+2z=1
2. kx+2y+4z=k

For what value of k does the system have an infinite number of solutions? Determine the solution to the system for this value of k.

anonymous · Answer

k=2 will give you two coincident lines, so infinity solutions

anonymous · Answer

yeah, that's my answer too
but the book says
that "the system will have an infinite number of solutions for $any\ value\ of\ k$"

loser66 · Answer

because you have a linear dependent system (2 equations, 3 variables) so, no matter what value of k is, the system has infinite solution set

anonymous · Answer

AAHhHHH! got it thanks (AGAIN)! :)