Answer:
a = 3 ; b = 4
Step-by-step explanation:
Eqn.1 = [tex] \frac{6}{a} - \frac{4}{b} = 1[/tex]
Eqn.2 = [tex] \frac{9}{a} - \frac{8}{b} = 1[/tex]
Both the eqns have RHS (Right Hand Side) equal. So,
[tex] \frac{6}{a} - \frac{4}{b} = \frac{9}{a} - \frac{8}{b} [/tex]
[tex] = > \frac{6b - 4a}{ab} = \frac{9b - 8a}{ab} [/tex]
Cancelling ab from both the denominators of both the sides,
[tex] = > 6b - 4a = 9b - 8a[/tex]
[tex] = > 8a - 4a = 9b - 6b[/tex]
[tex] = > 4a = 3b[/tex]
[tex] = > a = \frac{3b}{4} [/tex]
Putting the value of a in Eqn.1,
[tex] \frac{6}{ \frac{3b}{4} } - \frac{4}{b} = 1[/tex]
[tex] = > \frac{24}{3b} - \frac{4}{b} = 1[/tex]
[tex] = > \frac{8}{b} - \frac{4}{b} = 1[/tex]
[tex] = > \frac{8 - 4}{b} = 1[/tex]
[tex] = > b = 4[/tex]
Putting the value of b in the value of a
[tex]a = \frac{3 \times 4}{4} = 3[/tex]
