[tex]\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}[/tex]
well, clearly 50 ≠ 49.
but, whenever we get a result of this kind, is just a way to say no solutions.
you can look at it this way, is a system of equations, the equations are
y = -37z + 50
y = -37z + 49
now, notice, since both equations are in slope-intercept form, both equations have the same slope of -37, however, the y-intercept differs, meaning both equations are parallel and never touch each other.
since a solution for them is where they intercept and they never do, no solutions.
