# How do you solve the system a=3b+1 and 5b-2a=1?

##### 1 Answer
Dec 12, 2015

The solution for the system of equations is
color(blue)(a=-8,b=-3

#### Explanation:

a=color(blue)(3b+1........equation $\left(1\right)$

$5 b - 2 a = 1$......equation $\left(2\right)$

Solving by substitution

Substituting equation $1$ in $2$:

$5 b - 2 a = 1$

$5 b - 2 \cdot \left(\textcolor{b l u e}{3 b + 1}\right) = 1$

$5 b - 6 b - 2 = 1$

$- b = 1 + 2$

color(blue)(b=-3

Finding $a$ by substituting the value of $b$ in equation $1$:

$a = 3 b + 1$

$a = 3 \cdot - 3 + 1$

$a = - 9 + 1$

color(blue)(a=-8