For what negative value of k is there exactly one solution to the system of equations \(\begin{align*} y &= 2x^2 + kx + 6 \\ y &= -x + 4? \end{align*}\)
Substitute and simplify
2x2 + (k+1)x + 2
There is exactly one solution when the discriminate is equal to 0.
That is my hint and I will let you solve.