# How do solve the following linear system?:  3x-2y=2 , -4x-14y=28 ?

Feb 2, 2016

Solve by substitution and elimination:

$3 x - 2 y = 2$

$- 4 x - 14 y = 28$

We can eliminate $- 14 y$ from the second equation by $- 2 y$ from the first equation if we multiply it with $- 7$ to get $14 y$

$\rightarrow - 7 \left(3 x - 2 y = 2\right)$

Use distributive property:

$\rightarrow - 21 x + 14 y = - 14$

$\rightarrow \left(- 4 x - 14 y = 28\right) + \left(- 21 x + 14 y = - 14\right)$

$\rightarrow - 25 x = 14$

$\rightarrow x = - \frac{14}{25}$

Substitute the value of $x$ to the first equation:

$\rightarrow 3 \left(- \frac{14}{25}\right) - 2 y = 2$

$\rightarrow - \frac{42}{25} - 2 y = 2$

$\rightarrow - 2 y = 2 + \frac{42}{25}$

$\rightarrow - 2 y = \frac{92}{25}$

$\rightarrow y = \frac{92}{25} \div \left(- \frac{2}{1}\right)$

$\rightarrow y = \frac{92}{25} \cdot \left(- \frac{1}{2}\right)$

$\rightarrow y = - \frac{46}{25}$

So,
$\left(x , y\right) = \left(- \frac{14}{25} , - \frac{46}{25}\right)$ :)