For a certain value of k, the system

x + y + 3z = 10

-4x + 8y + 5z = 7

kx + z = 3

has no solutions. What is this value of k?

Guest Mar 4, 2023

#1**+1 **

x + y + 3z = 10 → y = 10 - x - 3z

(we want to get y by itself0

-4x + 2y +5z = 7 → -4x + 2(10 - x - 3z) + 5z = 7 → -4x + 20 -2x - 6z + 5z = 7 → -6x - z = -13 →

6x + z = 13

(substitute y into the second equation)

Notice we have this system now

k*x + z = 3

6x + z = 13

And notice that, if k =6, we would have this system:

6x + z = 3 and

6x + z = 13 but this is impossible, because two things added together can't possibly have two different outcomes

when k = 6, the system has no solution.

ChessChris Mar 5, 2023