What is 8/a-9/b =1,(10)/a+6/b =7 ?

The solution to 8/a-9/b =1,(10)/a+6/b =7 is

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8/a-9/b =1,(10)/a+6/b =7

\frac{8}{a} - \frac{9}{b} = 1, \frac{10}{a} + \frac{6}{b} = 7

(a = 2, b = 3)

Solution steps

[\frac{8}{a} - \frac{9}{b} = 1 \frac{10}{a} + \frac{6}{b} = 7]

Isolate

a

for

\frac{8}{a} - \frac{9}{b} = 1 : a = \frac{8 b}{9 + b}; b \neq = - 9

Plug the solutions

a = \frac{8 b}{9 + b}

into

\frac{10}{a} + \frac{6}{b} = 7

For

\frac{10}{a} + \frac{6}{b} = 7

, subsitute

a

with

\frac{8 b}{9 + b} : b = 3

Plug the solutions

b = 3

into

\frac{8}{a} - \frac{9}{b} = 1

For

\frac{8}{a} - \frac{9}{b} = 1

, subsitute

b

with

3 : a = 2

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{8}{a} - \frac{9}{b} = 1, \frac{10}{a} + \frac{6}{b} = 7

(a = 2, b = 3)

- x + y = 1, - 2 x + 2 y = 2

3 x - 2 y = 4, 2 x + 3 y = - 6

6 a + 3 b = 5, 3 a + 12 b = 13

x - 2 y + 7 = 0, x + y + 2 = 0

4 a - 3 b = 5, 3 a - 4 b = 2