System of equations,

3x - 6y = 2

5x + 4y = 1

3x-6y=2 (label equation 1)

5x+4y=1 (label equation 2)

-6y=-3x+2 (rearranged equation 1)

y=1/2x-1/3 (label equation 3)

substitute equation 3 into equation 2

5x+4 (1/2x-1/3) = 1

5x+2x-4/3=1

15x+6x-4=3 (multiplied everything by 3)

21x-4=3

+4 + 4

21x=7

x = 7/21

x=1/3

sub x=7/21 into equation 3

y = 1/2 (1/3) - 1/3

y = - 1/6

Therefore x=1/3 and y = - 1/6