Question 582390
First get the equations into the form
{{{ y = m*x + b }}} where {{{m}}} = slope
{{{ 5x + 2y = 6 }}}
{{{ 2y = -5x + 6 }}}
{{{ y = -(5/2)*x + 3 }}}
and
{{{ 3x = 2y - 12 }}}
{{{ 2y = 3x + 12 }}}
{{{ y = (3/2)*x + 6 }}}
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The slopes are different, which means 
the lines are not parallel.
This also means they are not the same line.
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In order to be perpendicular, the slopes must
be related like this:
{{{ m[1] = -( 1/m[2] ) }}}
For these slopes, {{{ -( 1/(3/2) ) = -(2/3) }}},
but the other slope is {{{ -(5/2) }}}
so the lines are not perpendicular.
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The only choice left is that they are different lines
Here's a plot of the lines:
{{{ graph( 400, 400, -10, 10, -10, 10, -(5/2)*x + 3, (3/2)*x + 6 ) }}}