Question 75688
First we need to solve both of these equations for y:
{{{x - 5y = 10}}}
{{{- 5y = 10-x}}} Subtract x from both sides
{{{y = -2+(1/5)x}}} Divide both sides by -5


{{{5x + y = 5}}} Subtract 5x from both sides
{{{y = 5-5x}}}

So we have two equations {{{y = 5-5x}}} and {{{y = -2+(1/5)x}}} with slopes
of {{{m=1/5}}} and {{{m=-5}}}. Since they are the negative inverse of each other (ie {{{m[p]=-1/m}}} where {{{m[p]}}} is the perpendicular slope), the two equations are perpendicular.