For a certain value of k, the system
\begin{align*}
x + y + 3z &= 10, \\
-4x + 3y + 5z &= 7, \\
kx + z &= 3
\end{align*}
has no solutions. What is this value of k?
+128473 x + y + 3z = 10
-4x + 3y + 5z = 7
kx + z = 3
Multiply the first equation through by -3
-3x - 3y - 9z = - 30
Add this to the second equation producing
-7x - 4z = - 22
Multiply the third given equation through by -4 producing
-4kx - 4z = -12
So notice that if -7 = - 4k , k = 7/4 we eill have no solutions because the system then becomes
-7x - 4z = -22
-7x - 4z = -12 The left side cannot simulataneously give different results on the right
So....no solutions when k = 7/4
