multiply first equation by 3,   3(2x+5y) =3(-9)

                                          6x+15y = -27

multiply second equation by -2,   -2(3x-4y) = -2(-2)

                                           -6x +8y = 4

If you add the two new equations: 6x-6x +15y+8y = -27+4  

                                                  23y = -23   , y = -1

Plugging in y= -1, in equation 1, 2x-5 = -9    , 2x = -4,   x = -2      (-2,-1) is your answer.