we should multiply the 1/18 above, by a number "n", such that our product is the 5/6 below, namely the x-coefficient in the 2nd equation, but with a different sign, positive.
[tex]\bf \begin{cases} \cfrac{1}{18}x+\cfrac{4}{5}y&=10\\[2em] -\cfrac{5}{6}x-\cfrac{3}{4}y&=3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{18}n=\cfrac{5}{6}\implies \cfrac{n}{18}=\cfrac{5}{6}\implies 6n=90\implies n=\cfrac{90}{6}\implies n=15 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{18}x(15)\implies \cfrac{15}{18}x\implies \cfrac{5}{6}x[/tex]
