Question

A system of linear equations contains two equations with negative reciprocal

Answer 1

let's recall that perpendicular lines have negative reciprocal slopes, so say for a line with a slope of a/b

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{a}{b}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{b}{a}}\qquad \stackrel{negative~reciprocal}{-\cfrac{b}{a}}}$

a perpendicular one will be -b/a.

what does that mean?  well, that the lines are perpendicular of course, they meet at a 90° angle, and two straight lines meeting at 90° can only meet once.

since a solution to a system of equations is where the graph meet, and these two meet  perpendicularly once, then that means only one solution.