Please help solve 3x+5y=-9 and 2x-3y=13

Please help solve the system 3x+5y=-9 and 2x-3y=13 by changing the augmented matrix to reduced echelon form. My math teacher said the answer is y=3 and x=-46. I think he made a mistake. Please help find the real answer. Thanks(please do not use the substitution method and check your answers)

6x = -18 - 10y

6x = 39 + 9y

-18 - 10y = 39 + 9y
-57 = 19y
y = -3

3x + 5(-3) = -9
3x = 6
x=2