Give a+34b=2 and b+34a=6 How do you find ba?

"Give a+34b=2 and b+34a=6 How do you find..." was answered by students like you

Pegov1

2022-02-03

Give

a + \frac{3}{4} b = 2

and

b + \frac{3}{4} a = 6

How do you find

\frac{b}{a}

lofia1r

Beginner2022-02-04Added 15 answers

Step 1
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 + 16 b = 96

3) Now, let us substract both equations:

- 7 b = - 72 \to b = \frac{72}{7}

4) We get a from the first equation:

a = 2 - \frac{3}{4} b = 2 - \frac{3}{4} \times \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}

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