First, substitute #color(red)(-5) and #color(blue)(-1)# for #color(red)(x) and #color(blue)(y)# in the first equation and see if both sides of the equation calculate to the same value:

#3color(blue)(y) = -2color(red)(x) - 13# becomes:

#3 xx color(blue)(-1) = (-2 xx color(red)(-5)) - 13#

#-3 = 10 - 13#

#-3 = -3#

The first, equation has #(-5, -1)# as a solution. Now, substitute #color(red)(-5) and #color(blue)(-1)# for #color(red)(x) and #color(blue)(y)# in the second equation and see if both sides of the equation calculate to the same value:

#-4color(red)(x) = -8color(blue)(y) + 12# becomes:

#-4 xx color(red)(-5) = (-8 xx color(blue)(-1)) + 12#

#20 = 8 + 12#

#20 = 20#