Question 285162
To do this you need to solve both equations for y, once you have done this you will be able to see the slopes and that will tell you if they are perpendicular.
So {{{5x-8y=3}}} add 8y to both sides.
{{{5x=8y+3}}} subtract 3 from both sides.
{{{5x-3=8y}}} And divide through by 8.
{{{(5/8)*x-3/8=y}}} So the slope is {{{m=5/8}}} that comes from the number attached to the x.
For the next equation.
{{{5y-8x=2}}} Add 8x to both sides.
{{{5y=8x+2}}} And divide through by 8.
{{{y=(8/5)*x+2/5}}}
So the slope is {{{m=8/5}}}
The definition for two lines to be perpendicular is that the slope of one must be the negative reciprocal of the slope of the other. The negative reciprocal of {{{5/8}}} is {{{-8/5}}} and we only got {{{8/5}}} so they are not perpendicular.