# How do you solve the system of equations algebraically 3/5x-1/6y=1, 1/5x+5/6y=11?

Aug 12, 2017

$y = 12 , x = 5$

#### Explanation:

$\frac{3}{5} x - \frac{1}{6} y = 1$------(1)

$\frac{1}{5} x + \frac{5}{6} y = 11$------(2)

$\therefore \left(1\right) \times 5$

$\therefore \left(5\right) \frac{3}{5} x - \left(5\right) \frac{1}{6} y = 5$

$\therefore \frac{15}{5} x - \frac{5}{6} y = 5$

$\therefore 3 x - \frac{5}{6} y = 5$------(3)

$\therefore \left(2\right) + \left(3\right)$

$\therefore 3 \frac{1}{5} x = 16$

$\therefore \frac{16}{5} x = 16$

$\therefore x = \frac{16}{\frac{16}{5}}$

$\therefore x = {\cancel{16}}^{1} / 1 \times \frac{5}{\cancel{16}} ^ 1$

:.color(magenta)(x=5

substitute color(magenta)(x=5 in(1)

$\therefore \frac{3}{5} \left(\textcolor{m a \ge n t a}{5}\right) - \frac{1}{6} y = 1$

$\therefore \frac{15}{5} - \frac{1}{6} y = 1$

$\therefore 3 - \frac{1}{6} y = 1$

$\therefore - \frac{1}{6} y = 1 - 3$

$\therefore - \frac{1}{6} y = - 2$

$\therefore y = \frac{2}{\frac{1}{6}}$

$\therefore y = 2 \times 6$

:.color(magenta)(y=12

substitute color(magenta)(y=12,x=5 in (2)

$\therefore \frac{1}{5} \left(\textcolor{m a \ge n t a}{5}\right) + \frac{5}{6} \left(\textcolor{m a \ge n t a}{12}\right) = 11$

$\therefore \frac{5}{5} + \frac{60}{6} = 11$

$\therefore 1 + 10 = 11$

:.color(magenta)(11=11