# How do solve the following linear system?:  x-y=11 , -4x-15y=-1 ?

May 3, 2016

The solution for the system of equations is:
color(green)( x = 166/ 19
color(green)(y = - 43/ 19

#### Explanation:

$x - y = 11$, multiplying by $4$

$\textcolor{b l u e}{4 x} - 4 y = 44$..............equation $\left(1\right)$

$\textcolor{b l u e}{- 4 x} - 15 y = - 1$.......equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$ , eliminates $\textcolor{b l u e}{4 x}$

$\cancel{\textcolor{b l u e}{4 x}} - 4 y = 44$
$\cancel{\textcolor{b l u e}{- 4 x}} - 15 y = - 1$

$- 19 y = 43$

$y = \frac{43}{- 19}$

color(green)(y = - 43/ 19

Finding the value of $x$ from equation $1$ using the value of $y$:

$x - y = 11$

$x = 11 + y$

 x = 11 color(green)(- 43/19

 x = 209 / 19 color(green)(- 43/19

color(green)( x = 166/ 19