# How do you solve the system of equations y= 2x + 8 and 3x + 5y = 1?

Jun 26, 2018

By arranging the equations

#### Explanation:

Arrange the equations (multiply the 1st by 3 and the 2nd by 2):

$3 y - 6 x = 24$
$6 x + 10 y = 2$

Combine these:
$13 y = 26$

$y = \frac{26}{13} = 2$

Put this in the first original equation:
$2 x = y - 8$

$2 x = 2 - 8$

$2 x = - 6$

$x = - 3$

Jun 26, 2018

$x = - 3$ and $y = 2$

#### Explanation:

After putting first equation into second,

$3 x + 5 \cdot \left(2 x + 8\right) = 1$

$13 x + 40 = 1$

$13 x = - 39$, so $x = - 3$

Thus, $y = 2 \cdot \left(- 3\right) + 8 = 2$