# How do you solve 3a - 2b = 8 and 4a + b = 7 using substitution?

Jul 4, 2017

From the second equation you may infer: $b = 7 - 4 a$

#### Explanation:

Now substitute $b$ in the first equation:

$3 a - 2 \left(7 - 4 a\right) = 8 \to 3 a - 14 + 8 a = 8 \to$

$3 a + 8 a = 8 + 14 \to 11 a = 22 \to a = \frac{22}{11} = 2$

$b = 7 - 4 \cdot 2 = - 1$

$3 \cdot 2 - 2 \cdot \left(- 1\right) = 6 + 2 = 8$ check!
$4 \cdot 2 + \left(- 1\right) = 8 - 1 = 7$ check!