# How do you determine the solution in terms of a system of linear equations for -2x + 3y = 14, x - 4y = 11?

Oct 6, 2015

$\left(x , y\right) = \left(- 17.8 , - 7.2\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXX}} - 2 x + 3 y = 14$
[2]$\textcolor{w h i t e}{\text{XXX}} x - 4 y = 11$

Multiply [2] by $2$
[3]$\textcolor{w h i t e}{\text{XXX}} 2 x - 8 y = 22$

[4]$\textcolor{w h i t e}{\text{XXX}} - 5 y = 36$

Divide [4] by $\left(- 5\right)$
[6]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{36}{5} = - 7.2$

Substituting $\left(7.2\right)$ for $y$ in [1]
[7]$\textcolor{w h i t e}{\text{XXX}} - 2 x + 3 \left(- 7.2\right) = 14$

[8]$\textcolor{w h i t e}{\text{XXX}} - 2 x - 21.6 = 14$

[9]$\textcolor{w h i t e}{\text{XXX}} - 2 x = 35.6$

[10]$\textcolor{w h i t e}{\text{XXX}} x = - 17.8$