### Instruction: The lines $-2x + y = k$ and $0.5x + y = 14$ intersect when $x = -8.4$. What is the value of $k$?### Response: To find the value of $k$, I need to know the coordinates of the point of intersection of the two lines.
I already have the $x$-coordinate, which is $-8.4$, so I just need to find the $y$-coordinate.
I can use either equation to do that, but I'll choose the second one because it has simpler coefficients.
Substituting $x = -8.4$ into the second equation, I get $0.5(-8.4) + y = 14$.
Simplifying, I get $-4.2 + y = 14$.
Adding $4.2$ to both sides, I get $y = 18.2$.
So the point of intersection is $(-8.4, 18.2)$.
Now that I have both coordinates, I can plug them into the first equation to find $k$.
Substituting $x = -8.4$ and $y = 18.2$ into the first equation, I get $-2(-8.4) + 18.2 = k$.
Simplifying, I get $16.8 + 18.2 = k$.