# How do you solve 2x+3y=2 and 6x+18y=9?

Sep 5, 2015

The solution is
color(blue)(x=1/2, y=1/3

#### Explanation:

$2 x + 3 y = 2$, multiplying this equation by $3$
$\textcolor{b l u e}{6 x} + 9 y = 6$......equation $1$

$\textcolor{b l u e}{6 x} + 18 y = 9$.....equation $2$

Solving by elimination.
Subtracting equation $2$ from $1$ eliminates color(blue)(6x

$\cancel{\textcolor{b l u e}{6 x}} + 9 y = 6$
$- \cancel{\textcolor{b l u e}{6 x}} - 18 y = - 9$

$- 9 y = - 3$
color(blue)(y=1/3

Finding $x$ by substituting $y$ in equation $1$:

$2 x + 3 y = 2$

$2 x = 2 - 3 y$

$2 x = 2 - 3 \cdot \frac{1}{3}$

$2 x = 2 - 1$

$2 x = 1$
color(blue)(x=1/2