# How do you solve the simultaneous equations a+5=b and 2a+3b=6?

Mar 26, 2018

$a = - \frac{9}{5}$
$b = \frac{16}{5}$

#### Explanation:

I sub one of the equations into the other.

$b = a + 5$
$2 a + 3 b = 6$

therefore

$2 a + 3 \left(a + 5\right) = 6$
$2 a + 3 a + 15 = 6$
$5 a = - 9$
$a = - \frac{9}{5}$

$b = 5 - \frac{9}{5}$
$b = \frac{16}{5}$

I used substitution method, in other cases it can be easier to use what's known as elimination.