Step 1) Solve the first equation for #y#:
#6x + 3y = 0#
#-color(red)(6x) + 6x + 3y = -color(red)(6x) + 0#
#0 + 3y = -6x#
#3y = -6x#
#(3y)/color(red)(3) = (-6x)/color(red)(3)#
#(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -2x#
#y = -2x#
Step 2) Substitute #(-2x)# for #y# in the second equation and solve for #x#:
#-5x + 2y = 27# becomes:
#-5x + 2(-2x) = 27#
#-5x + (-4x) = 27#
#-5x - 4x = 27#
#(-5 - 4)x = 27#
#-9x = 27#
#(-9x)/color(red)(-9) = 27/color(red)(-9)#
#(color(red)(cancel(color(black)(-9)))x)/cancel(color(red)(-9)) = -3#
#x = -3#
Step 3) Substitute #-3# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -2x# becomes:
#y = (-2 xx -3)#
#y = 6#
The Solution Is: #x = -3# and #y = 6# and #(-3, 6)#