How do we know when a system has no solutions?
Suppose $K$ is a constant, such that no pair of real numbers $(x,y)$ satisfies this system of equations: \begin{align*} 6x + 4y &= 7 \\ Kx + 4y &= 4 \end{align*} What is the value of $K$?
If the same system = two different values, then we have no solutions
So K = 6
Think about it
If 6x + 4y = 7 for some x, y
Then 6x + 4y CANNOT also = 4 for the same x, y !!!!
+1678 
