# How do you solve the following system: 5x+2y=20 , 3x+4y=-10 ?

Mar 3, 2016

#### Answer:

The solution for the system of equations is:

color(blue)(x=50/7

color(blue)(y = -55/7

#### Explanation:

$5 x + 2 y = 20$, multiplying by $2$
$10 x + \textcolor{b l u e}{4 y} = 40$.......equation $\left(1\right)$

$3 x + \textcolor{b l u e}{4 y} = - 10$.....equation $\left(2\right)$

Solving by elimination.

Subtracting equation $\left(2\right)$ from $\left(1\right)$ results in elimination of color(blue)(4y

$10 x + \cancel{\textcolor{b l u e}{4 y}} = 40$
$- 3 x - \cancel{\textcolor{b l u e}{4 y}} = 10$

$7 x = 50$

color(blue)(x=50/7

Finding $y$ from equation $1$

$5 x + 2 y = 20$

$2 y = 20 - 5 x$

$2 y = 20 - 5 \times \frac{50}{7}$

$2 y = 20 - \frac{250}{7}$

$2 y = \frac{140}{7} - \frac{250}{7}$

$2 y = - \frac{110}{7}$

$y = - \frac{110}{7 \times 2}$

color(blue)(y = -55/7