Question

How many solutions does the following equation have? 60z+50-97z=-37z+49

Answer 1

$\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}$

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.