Solve[br][br][math] \begin{cases}\begin{align}[br]2\frac{1}{5}x+3\frac{1}{10}y&=-3\frac{1}{2}\\[br]-\frac{7}{10}x+1\frac{4}{5}y&=-5\\[br]\end{align}\end{cases}[/math][br][br]First, we must rewrite mixec numbers as fraction numbers. Avoid decimal numbers, as they do not usually give exact solutions.[br][br][math] \begin{cases}\begin{align}[br]\frac{11}{5}x+\frac{31}{10}y&=-\frac{7}{2}\\[br]-\frac{7}{10}x+\frac{9}{5}y&=-5\\[br]\end{align}\end{cases}[/math][br][br]Secondly, multiply both equations with the least common multiplier of denominators to exclude them. [br][br][math] \begin{cases}\begin{align}[br]10\cdot\frac{11}{5}x+10\cdot\frac{31}{10}y&=10\cdot(-\frac{7}{2})\\[br]10\cdot(-\frac{7}{10}x)+10\cdot\frac{9}{5}y&=10\cdot(-5)\\[br]\end{align}\end{cases}[/math][br][br]Now, all multipliers are integer:[br][br][math] \begin{cases}\begin{align}[br]2\cdot 11 x+ 31 y&=5\cdot(-7)\\[br] -7x +2\cdot 9 y&=10\cdot(-5)\\[br]\end{align}\end{cases}\;\;\Leftrightarrow \;\;\begin{cases}\begin{align}[br]22 x+ 31 y&=-35&|\cdot 7\\[br] -7x +18 y&=-50&|\cdot 22\\[br]\end{align}\end{cases}.[/math][br] [br][br]Let us multiply equations so that multipliers of [i]x[/i] are opposite numbers:[br][br]  [math][br]\begin{cases}\begin{align}[br]154 x+ 217 y&=-245\\[br]-154x +396 y&=-1100\\[br]\end{align}\end{cases}[/math][br] [br]Solve linear equations of [i]y:[/i][br] [br][math]\begin{eqnarray}[br]613y&=&-1345\\[br]y&=&\frac{-1345}{613}\approx -2.2[br]\end{eqnarray}[/math][br] [br]and get value for [i]x[/i]:[br][br][math]\begin{array}{rcl}[br]-\frac{7}{10}x+\frac{9}{5}\dot(-\frac{1345}{613})&=&-5\\[br]-\frac{7}{10}x&=&-5+9\cdot \frac{269}{613}\\[br]x&=&-\frac{10}{7}\cdot(- \frac{644}{613})\\[br]x&=&\frac{920}{613}\approx 1.5[br]\end{array}[/math][br]