SAT Question 466b87e3: Systems of Linear Equations answer and explanation with Desmos solution

A system of two linear equations has no solution when the graphs of the equations have the same slope and different $y$-intercepts. Each of the given linear equations is written in the slope-intercept form, $y=mx+b$, where $m$ is the slope and $b$ is the $y$-coordinate of the $y$-intercept of the graph of the equation. For these two linear equations, the $y$-intercepts are $(0,8)$ and $(0,10)$. Thus, if the system of equations has no solution, the slopes of the graphs of the two linear equations must be the same. The slope of the graph of the first linear equation is $\frac{1}{2}$. Therefore, for the system of equations to have no solution, the value of $c$ must be $\frac{1}{2}$. Note that 1/2, .5, .50, and 0.5 are examples of ways to enter a correct answer.