Find the value of k that has NO possible solutions\(\begin{align*} x + y + 3z &= 10, \\ -4x + 2y + 5z &= 7, \\ kx + z &= 3 \end{align*}\)

Please help this my homework need to get it done quick

No need to show your work

Web2.0CalcUser123
Nov 3, 2018

#1**+1 **

LOL!!!...it would be hard to intuit this if some work weren't done !!!!

Multiply the first equation through by -2 and we have

-2x - 2y - 6z = -20 add this to the second equation and we get

-6x - z = -13 multiply this through by - 1

6x + z = 13 (1)

So..notice that if k = 6 we have

6x + z = 3 (2)

But (1) and (2) are parallel lines that never intersect.....so no solution is possible when k = 6

CPhill
Nov 3, 2018