Question 108605
L1 :{{{x-2y=10}}}
L2 :{{{2x + y = 2}}}
Re-arrange your equations into the slope-interept form. 
L1 :{{{x-2y=10}}}
L1 :{{{-2y=10-x}}}
L1 :{{{y=x/2-5}}}
L2 :{{{2x+y=2}}}
L2 :{{{y=-2x+2}}}
Slope of L1 is {{{m[1]=1/2}}}.
Slope of L2 is {{{m[2]=-2}}}.
Parallel lines have equal slopes.
{{{m[1]=m[2]}}}
Perpendicular lines have slope that are negative reciprocals. 
{{{m[1]=(-1)/m[2]}}}
Since
{{{1/2=(-1)/(-2)}}}
L1 and L2 are perpendicular.