# How do you solve 2/3x - 3y = 1/5 and 2x - 9y = 4?

Sep 11, 2015

The two lines are parallel to each other. It has no solution.

#### Explanation:

$\frac{2}{3} x - 3 y = \frac{1}{5}$ --------(1)
$2 x - 9 y = 4$ -------------(2)

Multiply each term in equation (1) by 3
$\frac{2}{3} x - 3 y = \frac{1}{5}$ --------(1)$\times 3$
$2 x - 9 y = \frac{3}{5}$ --------(3)

The co-efficients of x and y in the 2nd equations are 3 times the co-efficients of x and y of the 1st equation.

Moreover the equation in the general form. Its slope is given by -a/b) provided the equation is in the form $a x + b y = c$

The slope of the 1st line is $= - \frac{2}{3} \times - 3 = \frac{9}{2}$
The slope of the 2nd line is$= - \left(\frac{2}{- 9}\right) = \frac{2}{9}$

Hence it has no solution.

Refer the graph also