substitution

4x + 3y = 3
7x - 9y = 6

1 answer

from the 1st
3y = 3-4x
or 9y = 9 - 12x

now sub that into the 2nd
7x - (9-12x) = 6
19x = 15
x = 15/19

back into 3y = 3-4x
3y = 3 - 60/19 = -3/19
y = -1/19