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

Aug 21, 2015

The solutions are
color(blue)(a=1,b=-1

#### Explanation:

 2a+3b=−1 , multiplying the equation by $3$
 color(blue)(6a)+9b=−3 ..........equation $1$

 3a+5b=−2multiplying the equation by $2$
color(blue)( 6a)+10b=−4.......equation $2$

Solving by elimination .
Subtracting equation $2$ form $1$

cancel( color(blue)(6a))+9b=−3
$\cancel{- \textcolor{b l u e}{6 a}} - 10 b = + 4$

$- b = 1$
color(blue)(b=-1

Substituting $b$ in equation $1$ to find $a$:
2a+3b=−1
2a=−1-3b
2a=−1-3*(-1)
$2 a = 2$
color(blue)(a=1