Question 39950
1st: 6x+3y=0
2nd: 8x+5y=3

Multiply 1st by 5 and 2nd by 3 to get rid of the y-terms.

1st: 30x+15y=0
2nd: 24x+15y=9

Subtract the 2nd from the 1st to get:
3rd: 6x=-9
     x=-3/2
Substitute that value into the original 1st equation (or 2nd).
6(-3/2)+3y=0
-9+3y=0
3y=9
y=3
SOLUTION:
x=-3/2; y=3
Check this in the 2nd original equation.
24(-3/2)+15(3)=9
-36+45=9
9=9
Cheers,
stan H.