# How do you solve using elimination of 3x=10-2y and 5x-6y+30=0?

Jun 13, 2018

$x = 0$
$y = 5$

#### Explanation:

$3 x = 10 - 2 y$ --- (1)
$5 x - 6 y + 30 = 0$ --- (2)

From (1)
$3 x = 10 - 2 y$
$x = \frac{1}{3} \left(10 - 2 y\right)$ --- (3)

Sub (3) into (2)
$5 \times \frac{1}{3} \left(10 - 2 y\right) - 6 y + 30 = 0$
$\frac{5}{3} \left(10 - 2 y\right) - 6 y + 30 = 0$
$\frac{50}{3} - \frac{10}{3} y - 6 y + 30 = 0$
$\frac{140}{3} - \frac{28}{3} y = 0$
$140 - 28 y = 0$
$140 = 28 y$
$y = 5$ --- (4)

Sub (4) into (3)
$x = \frac{1}{3} \left(10 - 2 y\right)$
$x = \frac{1}{3} \left(10 - 10\right)$
$x = 0$

Jun 13, 2018

$x = 0 , y = 5$

#### Explanation:

Multiplying the first equation by $3$ and adding to the second we get
$14 x = 0$
so
$x = 0$
with this result we get
$y = 5$