# How do solve the following linear system?:  2x+6y=5 , x-7y=4 ?

Feb 9, 2016

x=2 19/20; y=-3/20

#### Explanation:

$2 x + 6 y = 5 \left(1\right)$
$x - 7 y = 4 \left(2\right)$ Multiplying Equation (2) by 2 and then subtracting from equation (1) We get
$2 x + 6 y = 5 \left(1\right)$
$2 x - 14 y = 8 \left(2\right)$

$20 \cdot y = - 3$ $\therefore y = - \frac{3}{20} \mathmr{and} x = 4 + 7 \cdot \left(- \frac{3}{20}\right) = 4 - \frac{21}{20} = \frac{59}{20}${Ans]

Feb 9, 2016

$x , y = 2 \frac{19}{20} , - \frac{3}{20}$

#### Explanation:

Solve by elimination:

$\textcolor{b l u e}{2 x + 6 y = 5} , \textcolor{g r e e n}{x - 7 y = 4}$

We can eliminate $2 x$ from the first equation by $x$ in the second equation by multiplying it with $- 2$ to get $- 2 x$.

$\rightarrow - 2 \left(x - 7 y = 4\right)$

$\rightarrow - 2 x + 14 y = - 8$

$\rightarrow \left(2 x + 6 y = 5\right) + \left(- 2 x + 14 y = - 8\right)$

$\rightarrow 20 y = - 3$

$\rightarrow y = - \frac{3}{20}$

Substitute the value to the first equation:

$\rightarrow 2 x + 6 \left(- \frac{3}{20}\right) = 5$

$\rightarrow 2 x + \left(- \frac{18}{20}\right) = 5$

$\rightarrow 2 x + \left(- \frac{9}{10}\right) = 5$

$\rightarrow 2 x - \frac{9}{10} = 5$

$\rightarrow 2 x = 5 + \frac{9}{10}$

$\rightarrow 2 x = \frac{59}{10}$

$\rightarrow x = \frac{59}{10} \div 2$

$\rightarrow x = \frac{59}{10} \cdot \frac{1}{2}$

$\rightarrow x = \frac{59}{20} = 2 \frac{19}{20}$