# How do you solve x = 2y - 2 and 3x - y = 14 using substitution?

Apr 27, 2018

$\left(x , y\right) \to \left(6 , 4\right)$

#### Explanation:

$x = 2 y - 2 \to \left(1\right)$

$3 x - y = 14 \to \left(2\right)$

$\text{equation "(1)" expresses x in terms of y}$

$\textcolor{b l u e}{\text{Substitute "x=2y-2" into equation }} \left(2\right)$

$\Rightarrow 3 \left(2 y - 2\right) - y = 14$

$\Rightarrow 6 y - 6 - y = 14$

$\Rightarrow 5 y - 6 = 14$

$\text{add "6" to both sides}$

$\Rightarrow 5 y = 20 \Rightarrow y = \frac{20}{5} = 4$

$\text{substitute "y=4" into equation } \left(1\right)$

$\Rightarrow x = \left(2 \times 4\right) - 2 = 6$

$\text{the point of intersection of the 2 equations } = \left(6 , 4\right)$
graph{(y-1/2x-1)(y-3x+14)((x-6)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}