$\left\{{{10x-9y=1}\atop{15x+21y=36}}\right.$
$\Leftrightarrow \left\{{{30x-27y=3}\atop{30x+42y=72}}\right.$
$\Leftrightarrow \left\{{{-69y=-69}\atop{30x+42y=72}}\right.$
$\Leftrightarrow \left\{{{y=1}\atop{30x+42.1=72}}\right.$
$\Leftrightarrow \left\{{{x=1}\atop{y=1}}\right.$