I'm going to use elimination to solve this set of equations.
#-6x-5y=10#
#+-#
#3x-2y=-6#
I want to add or subtract the #y#s so that I will be left with only #x# as my variaable. To do that, I need to make the #y#s equal, so I'm going to multiply the second equation by #2.5#, becauase that will change #-2y# into #-5y#. Of course, I have to multiply everything by #2.5#, so the second equation will now be #7.5x-5y=-15#.
Now we have
#color(white)(.....)-6xcancel(-5y)=10#
#-#
#color(white)(........)7.5xcancel(-5y)=-15#
#color(white)(.)#_________
#color(white)(.....)-13.5x=color(white)(......)25#
We are left with #-13.5x=25#. Divide by #-13.5# on both sides, and we have #x=25/-13.5#, which we'll rewrite as #-50/27#.
