To solve this system of equations, we will first manipulate the first equation so that #y# is alone on the left-hand side of the equation.

#2x - 5y = 3#,

#-5y = 3 - 2x#,

#5y = -3 + 2x#,

#5y = 2x - 3#,

#y = 2/5 x - 3/5#.

We now plug this value of #y# into the second equation.

#3x - 6y = 9#,

#3x - 6(2/5 x - 3/5) = 9#,

#3x - 12/5 x + 18/5 = 9#.

Move all the #x#'s to one side of the equation and the constants to the other.

#3x - 12/5 x + 18 /5 = 9#,

#3x - 12/5 x = 9 - 18/5#.

Multiplying both sides of the equation by #5# makes it easier to manipulate.

#5(3x - 12/5 x) = 5(9 - 18 / 5)#,

#15x - 12x = 45 - 18#,

#3x = 27#,

#x = 9#.

Now plug this #x# back into the first equation.

#2x - 5y = 3#,

#2(9) - 5y = 3#,

#18 - 5y = 3#,

#18 = 3 + 5y#,

#15 = 5y#,

#3 = y#.

Thus, we have #x=9# and #y=3#.