Question 768212
These are 2 different equations, because
if you double the 1st one, you get
{{{ 2x + 4y = 20 }}}, which is not the 2nd one
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Now determine if they have the same slope, 
which will mean that they don't intersect, and
there will be no solution
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(1) {{{ x + 2y = 10 }}}
(1) {{{ 2y = -x + 10 }}}
(1) {{{ y = (-1/2)*x + 5 }}}
and
(2) {{{ 2x + 4y = 10 }}}
(2) {{{ 4y = -2x + 10 }}}
(2) {{{ y = (-1/2)*x + 5/2 }}}
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Both equations have a slope = {{{ -1/2 }}},
so they do not intersect, and there is no solution
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Here's a plot:
{{{ graph( 400, 400, -4, 12, -4, 12, (-1/2)*x + 5, (-1/2)*x + 5/2 ) }}}