Given $a + \frac{3}{4} b = 2$ $a+3/4b=2$ and $b + \frac{3}{4} a = 6$ $b+3/4a=6$ . How do you find $\frac{b}{a}$ $b/a$ ?

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Given $a + \frac{3}{4} b = 2$ $a+3/4b=2$ and $b + \frac{3}{4} a = 6$ $b+3/4a=6$ . How do you find $\frac{b}{a}$ $b/a$ ?

1 Answer

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Answer 1 · 2015-12-26T00:52:11

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

Explanation:

Let us solve the system by the row reduction method.

Let us multiply both equations by 4, in order to quit every fraction:
$4 a + 3 b = 8$ $4a+3b=8$
$3 a + 4 b = 24$ $3a+4b=24$
Now, let us multiply the first equation by 3 and the second one by 4, in order to get the same coefficient for $a$ $a$ :
$12 a + 9 b = 24$ $12 a + 9b = 24$
$12 a + 16 b = 96$ $12a+16b=96$
Now, let us substract both equations:
$- 7 b = - 72 \to b = \frac{72}{7}$ $-7b=-72 rightarrow b = 72/7$
We get $a$ $a$ from the first equation:
$a = 2 - \frac{3}{4} b = 2 - \frac{3}{4} \cdot \frac{72}{7} = - \frac{40}{7}$ $a = 2 - 3/4 b = 2 - 3/4 cdot 72/7 = -40/7$

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

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Given $a + \frac{3}{4} b = 2$ $a+3/4b=2$ and $b + \frac{3}{4} a = 6$ $b+3/4a=6$ . How do you find $\frac{b}{a}$ $b/a$ ?

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Explanation:

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Given $a + \frac{3}{4} b = 2$ $a+3/4b=2$ and $b + \frac{3}{4} a = 6$ $b+3/4a=6$ . How do you find $\frac{b}{a}$ $b/a$ ?