# How do you solve the following linear system 3x-2y=8, 2x-3y=-6 ?

Jun 9, 2016

(x,y)=color(green)(""(7.2,6.8))

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x - 2 y = 8$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y = - 6$

Multiplying [1] by $3$ and [2] by $2$
[3]$=$[1]$\times 3 \textcolor{w h i t e}{\text{XXX")9x-6y=color(white)("XX}} 24$
[4]$=$[2]$\times 2 \textcolor{w h i t e}{\text{XXX}} \underline{4 x - 6 y = - 12}$

Subtracting [4] from [5]
[6]$=$[5]$-$[4]$\textcolor{w h i t e}{\text{XXX}} 5 x = 36$

Dividing both sides by $5$
[7]$=$[6]$\div 5 \textcolor{w h i t e}{\text{XXX}} x = 7.2$

Substituting $7.2$ for $x$ in [1]
[8]$\textcolor{w h i t e}{\text{XXXXXX}} 3 \left(7.2\right) - 2 y = 8$
Simplifying
[9]$\textcolor{w h i t e}{\text{XXXXXX}} 21.6 - 2 y = 8$

[10]$\textcolor{w h i t e}{\text{XXXXXX}} 2 y = 13.6$

[11]$\textcolor{w h i t e}{\text{XXXXXX}} y = 6.8$

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For verification purposes substitute $\left(x , y\right) = \left(7.2 , 6.8\right)$ into [2]
$\textcolor{w h i t e}{\text{XXXXXXX}} 2 x - 3 y$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}} = 2 \left(7.2\right) - 3 \left(6.8\right)$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}} = 14.2 - 20.4$

$\textcolor{w h i t e}{\text{XXXXXXXXXX")=-6color(white)("XXX}}$as given.