The graph of a quadratic equation $y=a{x}^2+bx+c$ and a linear equation $y=mx+k$ are shown in the $xy$-plane above. If the linear equation is changed to $y=mx+k^{\prime }$, where $k^{\prime }$ is a value such that the new line is parallel to the original line but shifted vertically upwards, and the new line does not intersect the parabola, how many solutions would the new system of equations have?