Question

Solve for the values of r and s.

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Answer 1

Check the picture below.

`4r-s=2s-6r\implies 10r-s=2s\implies 10r=3s\implies r=\cfrac{3s}{10} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{\left[ 4\left( (3s)/(10) \right)-s \right]+\left[ 6\left( (3s)/(10) \right)+7s \right]}=180\implies \left( \cfrac{12s}{10}-s \right)+\left( \cfrac{18s}{10}+7s \right)=180 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}~\hfill }{10\left[ \left( \cfrac{12s}{10}-s \right)+\left( \cfrac{18s}{10}+7s \right) \right]=10(180)}`

`(12s-10s)+(18s+70s)=1800\implies \implies 90s=1800 \\\\\\ s=\cfrac{1800}{90}\implies \boxed{s=20} \\\\\\ \stackrel{\textit{we know that}}{r=\cfrac{3s}{10}}\implies r=\cfrac{3(20)}{10}\implies \boxed{r=6}`