Make #x# or #y# the subject and then substitute that in one of the equation.
#-6x+10y=5# -----> equation 1
#-2x+3y=-1# ------> equation 2
Lets make #x# the subject in equation 1:
#-6x+10y=5#
#-6x = 5-10y#
#x=-5/6+10/6y# ------> substitute #x# in equation 2
#-2x+3y=-1# ------> equation 2
#-2(-5/6 + 10/6y) + 3y = -1#
#5/3-10/3y+3y=-1#
#3y-10/3y = -1-5/3#
#(9y-10y)/3 = (-3-5)/3#
#-1/3y = -8/3#
#y = -8/3 xx (-3)#
#y=8#
Substitute #y=8# in equation 2 to get value of #y#.
#-2x+3y=-1# ------> equation 2
#-2x +3(8) = -1#
#-2x+24=-1#
#-2x = -1-24#
#-2x = -25#
#x=25/2#
Check the answer:
#-6x+10y=5# -----> equation 1
#-6(25/2) + 10(8) = 5
#-75+80 = 5# ----> correct