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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 $K$?

 Aug 18, 2023
 #1
avatar+129487 
+1

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   !!!!

 

cool cool cool

 Aug 18, 2023

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