# How do you solve the following system?: 6x - 4y = 3 , 5x - 2y = 1

Dec 2, 2015

$x = \frac{- 1}{4}$
$y = \frac{- 9}{8}$

#### Explanation:

$6 x - 4 y = 3$ --------------(1)
$5 x - 2 y = 1$ ------------------(2)
Let us have the equations as -

We are going to eliminate $y$

Before that understand $- 4 y + 4 y = 0$

Multiply equation (2) with $- 2$

$6 x - 4 y = 3$ ------------------(1)
$- 10 x + 4 y = - 2$ ------------------(2)

Add (1) and (2), we get -

$- 4 x = 1$
$x = \frac{- 1}{4}$

Substitute $x = \frac{- 1}{4}$ in equation (1)

$6 \left(\frac{- 1}{4}\right) - 4 y = 3$
$\frac{- 6}{4} - 4 y = 3$
$\frac{- 3}{2} - 4 y = 3$
$- 4 y = 3 + \frac{3}{2} = \frac{6 + 3}{2} = \frac{9}{2}$
$y = \frac{9}{2} \times \frac{1}{- 4} = \frac{- 9}{8}$