# How do you solve the system a+b=11 and 3a-2b=8?

Jul 31, 2018

$\left(a , b\right) \to \left(6 , 5\right)$

#### Explanation:

$a + b = 11 \to \left(1\right)$

$3 a - 2 b = 8 \to \left(2\right)$

$\text{from equation } \left(1\right) \textcolor{w h i t e}{x} a = 11 - b \to \left(3\right)$

$\text{substitute "a=11-b" into equation } \left(2\right)$

$3 \left(11 - b\right) - 2 b = 8$

$33 - 3 b - 2 b = 8$

$33 - 5 b = 8$

$\text{subtract 33 from both sides}$

$- 5 b = 8 - 33 = - 25$

$\text{divide both sides by } - 5$

$b = \frac{- 25}{- 5} = 5$

$\text{substitute "b=5" into equation } \left(3\right)$

$a = 11 - 5 = 6$

$\text{solution is } \left(a , b\right) \to \left(6 , 5\right)$