The lines -2x + y = k and 0.5x + y = 14 intersect when x = -8.4. What is the value of k?

Rearrange the equations to get y = ...

 

-2x + y = k  becomes  y = k + 2x                 (1)

0.5x + y = 14 becomes  y = 14 - 0.5x          (2)

 

Now equate (1) and (2)

k + 2x = 14 - 0.5x   or  k = 14 - 2.5x  (3)

 

Replace x in (3) by -8.4 to find k.