How do you solve y= 3/4x+3 and 2x-4y=6?

Sep 9, 2015

$\left(x , y\right) = \left(- 18 , - \frac{21}{2}\right)$

Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} y = \frac{3}{4} x + 3$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x - 4 y = 6$

Using [1], substitute $\frac{3}{4} x + 3$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 2 x - 4 \left(\frac{3}{4} x + 3\right) = 6$

[4]$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 x - 12 = 6$

[5]$\textcolor{w h i t e}{\text{XXX}} - x = 18$

[6]#color(white)("XXX")x = -18

Substitute $\left(- 18\right)$ for $x$ in[2]
[7]$\textcolor{w h i t e}{\text{XXX}} 2 \left(- 18\right) - 4 y = 6$

[8]$\textcolor{w h i t e}{\text{XXX}} - 4 y = 42$

[9]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{21}{2}$

Sep 9, 2015

$x = - 18$
$y = - \frac{21}{2}$

Explanation:

$y = \frac{3}{4} x + 3$---------------(1)
$2 x - 4 y = 6$-----------------(2)

Substitute the value of y from equation (1) in equation (2)

$2 x - 4 \left(\frac{3}{4} x + 3\right) = 6$
$2 x - 3 x - 12 = 6$
$- x = 6 + 12 = 18$
$x = - 18$

Substitute x value in equation (2)

$2 \left(- 18\right) - 4 y = 6$
$- 36 - 4 y = 6$
$- 4 y = 6 + 36 = 42$
$y = \frac{42}{-} 4 = - \frac{21}{2}$