Question

3/4x-1/2y=12 ax-by=9
what is the value of a/b

Answer 1

Explanation:

Hello,

I assume that we are looking for a and b so that

ax - by = 9

<=>

`(3)/(4)x-(1)/(2)y=12`

we can notice that 12 = 4 * 3

so we need to multiply by 3 and divide by 4 to get 9 from 12

`(3)/(4)*((3)/(4)x-(1)/(2)y)=(3)/(4)*12=9\\<=> (3*3)/(4*4)x-(1*3)/(4*2)y=9\\<=> (9)/(16)x-(3)/(8)y=9`

Then, we can identify a and b

`a=(9)/(16) \ \ \text{\sf and} \ \ b=(3)/(8)`

Then

`(a)/(b)=(9*8)/(16*3)=(3)/(2)`

hope this helps

Answer 2

3/2

Explanation:

3/4x - 1/2y = 12

*3/4 *3/4 *3/4

9/16x - 3/8y = 9

(9/16)/(3/8) = 9/16 * 8/3 = 3/2