# How do you solve the following system?: 5x + 2y =1 , -8x+3y=12

Jun 23, 2017

$\left(- \frac{21}{31} , \frac{68}{31}\right)$

#### Explanation:

$5 x + 2 y = 1$
$- 8 x + 3 y = 12$

The best way to solve this system of equations is by using the elimination method. Basically, we need to eliminate a variable by adding the two equations together.

However, to completely cancel out a variable, such as $x$, they need to have the same coefficient but different signs (positive and negative).

$8 \left(5 x + 2 y\right) = \left(1\right) 8$
$5 \left(- 8 x + 3 y\right) = \left(12\right) 5$

$40 x + 16 y = 8$
$- 40 x + 15 y = 60$

By multiplying the equations, we can now safely eliminate $x$ from the system by adding the two equations together.

$31 y = 68$

$y = \frac{68}{31}$

Now, you have to plug $y$ back into one of the equations to get $x$.

$5 x + 2 \left(\frac{68}{31}\right) = 1$

$5 x + \frac{136}{31} = 1$

$5 x = 1 - \frac{136}{31}$

$5 x = - \frac{105}{31}$

$x = - \frac{105}{31} \cdot \frac{1}{5}$

$x = - \frac{21}{31}$

$\left(- \frac{21}{31} , \frac{68}{31}\right)$