Answer:
Step-by-step explanation:
Hello,
I assume that we are looking for a and b so that
ax - by = 9
<=>
[tex]\dfrac{3}{4}x-\dfrac{1}{2}y=12[/tex]
we can notice that 12 = 4 * 3
so we need to multiply by 3 and divide by 4 to get 9 from 12
[tex]\dfrac{3}{4}*(\dfrac{3}{4}x-\dfrac{1}{2}y)=\dfrac{3}{4}*12=9\\<=> \dfrac{3*3}{4*4}x-\dfrac{1*3}{4*2}y=9\\<=> \dfrac{9}{16}x-\dfrac{3}{8}y=9[/tex]
Then, we can identify a and b
[tex]a=\dfrac{9}{16} \ \ \text{\sf and} \ \ b=\dfrac{3}{8}[/tex]
Then
[tex]\dfrac{a}{b}=\dfrac{9*8}{16*3}=\dfrac{3}{2}[/tex]
hope this helps
