# How do you solve the following linear system:  y=2x-1, x-y=5 ?

Dec 13, 2015

The solution for the system of equations is
color(blue)(x=-4,y=-9

#### Explanation:

color(blue)(y=2x-1.......equation $\left(1\right)$

$x - y = 5$.........equation $\left(2\right)$

Solving by substitution.

Substituting equation $1$ in equation $2$

$x - y = 5$

x-color(blue)((2x-1)=5

$x - 2 x + 1 = 5$

$- x + 1 = 5$

$- x = 5 - 1$

$- x = 4$

color(blue)(x =-4

Finding $y$ by substituting $x$ in equation $1$:

color(blue)(y=2x-1

$y = 2 \cdot \left(- 4\right) - 1$

$y = - 8 - 1$

color(blue)(y=-9