# Given a+3/4b=2 and b+3/4a=6. How do you find b/a?

Dec 26, 2015

Just solving the system would make possible to calculate $\frac{b}{a}$.

#### Explanation:

Let us solve the system by the row reduction method.

1. Let us multiply both equations by 4, in order to quit every fraction:
$4 a + 3 b = 8$
$3 a + 4 b = 24$

2. Now, let us multiply the first equation by 3 and the second one by 4, in order to get the same coefficient for $a$:
$12 a + 9 b = 24$
$12 a + 16 b = 96$

3. Now, let us substract both equations:
$- 7 b = - 72 \rightarrow b = \frac{72}{7}$

4. We get $a$ from the first equation:
$a = 2 - \frac{3}{4} b = 2 - \frac{3}{4} \cdot \frac{72}{7} = - \frac{40}{7}$

This way, the division $\frac{b}{a}$ equals $\frac{\frac{72}{7}}{- \frac{40}{7}} = - \frac{72}{40} = - \frac{9}{5}$