# How do you solve the system of equations algebraically x=2y-8, 2x-y=-7?

Nov 14, 2017

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

#### Explanation:

$x = 2 y - 8 \to \left(1\right)$

$2 x - y = - 7 \to \left(2\right)$

$\text{equation "(1)" gives x in terms of y so substitute into } \left(2\right)$

$\Rightarrow 2 \left(2 y - 8\right) - y = - 7$

$\Rightarrow 4 y - 16 - y = - 7$

$\Rightarrow 3 y = 9 \Rightarrow y = 3$

$\text{substitute this value into equation } \left(1\right)$

$x = \left(2 \times 3\right) - 8 = - 2$

$\text{point of intersection } = \left(- 2 , 3\right)$
graph{(y-1/2x-4)(y-2x-7)=0 [-10, 10, -5, 5]}