# How do you solve 7a=3-5b  and 2a+b=0?

May 9, 2016

The solution for the system of equations is:
color(green)(a = -1

color(green)(b = 2

#### Explanation:

$7 a = 3 - 5 b$..........equation $\left(1\right)$

$2 a + b = 0$

color(green)(b = -2a..............equation $\left(2\right)$

Solving by substitution:

Substituting equation $2$ in $1$:

$7 a = 3 - 5 b$

$7 a = 3 + \left(- 5\right) \cdot \textcolor{g r e e n}{\left(- 2 a\right)}$

$7 a = 3 + 10 a$

$7 a - 10 a = 3$

$- 3 a = 3$

$a = \frac{3}{- 3}$

color(green)(a = -1

Finding $b$ from equation $2$ :

$b = - 2 a$

$b = - 2 \cdot \left(- 1\right)$

color(green)(b = 2