# How do solve the following linear system?:  2x+7=-5y , 6x+4y=-1 ?

Jan 9, 2016

The solution for the system of equations is

color(blue)(x=23/22

color(blue)(y=-20/11

#### Explanation:

$2 x + 5 y = - 7$ ,multiplying by $3$

$\textcolor{b l u e}{6 x} + 15 y = - 21$ ........equation$1$

$\textcolor{b l u e}{6 x} + 4 y = - 1$...............equation$2$

Solving by elimination

Subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{6 x}} + 15 y = - 21$
$- \cancel{\textcolor{b l u e}{6 x}} - 4 y = 1$

$11 y = - 20$

color(blue)(y=-20/11

Finding $x$ from equation $1$:
$2 x + 5 y = - 7$

$2 x = - 7 - 5 y$

$2 x = - 7 - 5 \times \left(- \frac{20}{11}\right)$

$2 x = - 7 + \frac{100}{11}$

$2 x = - \frac{77}{11} + \frac{100}{11}$

$2 x = \frac{23}{11}$

$x = \frac{23}{11 \times 2}$

color(blue)(x=23/22