# How do you solve the following system:  7x − 5y = −11, 7x - y = 10 ?

Jan 3, 2016

color(blue)(x=61/28, y=21/4

#### Explanation:

$\textcolor{b l u e}{7 x} - 5 y = - 11$....equation $1$

$\textcolor{b l u e}{7 x} - y = 10$.....equation $2$

Solving by elimination

Subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{7 x}} - 5 y = - 11$

$- \cancel{\textcolor{b l u e}{7 x}} + y = - 10$

$- 4 y = - 21$

$y = \frac{- 21}{- 4}$

color(blue)(y=21/4

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

$7 x - 5 y = - 11$

$7 x = - 11 + 5 y$

$7 x = - 11 + 5 \times \left(\frac{21}{4}\right)$

$7 x = - 11 + \left(\frac{105}{4}\right)$

$7 x = - \frac{44}{4} + \left(\frac{105}{4}\right)$

$7 x = \frac{61}{4}$

color(blue)(x=61/28

The solution for the system of equations is :

color(blue)(x=61/28, y=21/4