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The lines  -2x + y = k  and  0.5x + y = 14  intersect when  x = -8.4 .

 

So when  x = -8.4 , both lines have the same  y  value.

Let's plug in  -8.4  for  x  into the second equation to find  y .

 

0.5(-8.4) + y = 14 

-4.2 + y  =  14

y  =  18.2

 

Now we found  x  and  y . Use these values in the first equation to find  k .

 

-2(-8.4) + 18.2  =  k

35  =  k