# How do you solve the system of equations a + 3b = 13 and a + b = 5?

Oct 17, 2017

$a = 1 , b = 4$

#### Explanation:

another way is by elimination

$a + 3 b = 13 - - \left(1\right)$

$a + b = 5 - - \left(2\right)$

subtract $\left(2\right) - \left(1\right)$

$2 b = 8 \implies b = 4$

substituting into (2)

$a + 4 = 4 \implies a = 1$

$a = 1 , b = 4$

check for consistency in $\left(1\right)$

1+3xx4=1+12=13sqrt#