# How do you solve the system of equations 6x - 2y = 1 and 2y - 10x = - 5?

Mar 27, 2017

$x = 1$ and $y = \frac{5}{2}$ or$2 \frac{1}{2}$

#### Explanation:

$\therefore 6 x - 2 y = 1$--------$\left(1\right)$

$\therefore - 10 x + 2 y = - 5$------$\left(2\right)$

$\therefore \left(1\right) + \left(2\right)$:

$\therefore - 4 x = - 4$

multiply L.H.S. and R.H.S. by $- 1$

$\therefore 4 x = 4$

$\therefore x = 1$

substitute $x = 1$ in -----$\left(1\right)$

$\therefore 6 \left(1\right) - 2 y = 1$

$\therefore 6 - 2 y = 1$

$- 2 y = 1 - 6$

multiply L.H.S. and R.H.S. by $- 1$

$\therefore 2 y = - 1 + 6$

$\therefore 2 y = 5$

$\therefore y = \frac{5}{2}$ or$2 \frac{1}{2}$

check:

substitute $x = 1$and $y = \frac{5}{2}$ in -----$\left(1\right)$

$\therefore 6 \left(1\right) - 2 \left(\frac{5}{2}\right) = 1$

$\therefore 6 - \frac{10}{2} = 1$

$\therefore 6 - 5 = 1$

$\therefore 1 = 1$