Let
#-3x - 3y = 3#
be eqn #(1)# and let
#y = -5x -17#
be eqn #(2)#. By means of substitution, we substitute eqn #(2)# into eqn #(1)# to find the unknown, #x#.
We arrive at:
#-3x -3(-5x - 17) = 3#
#-3x + 15x + 51 = 3#
#15x - 3x = 3 - 51#
#12x = -48#
#x = (-48)/12#
#x = -4#
We now have the value of #x#, hence we can substitute #x=-4# in eqn #(2)# to find the unknown #y#. By doing this, we arrive at:
#y = -5(-4) - 17#
#y = 20 - 17#
#y = 3#
Hence #x= -4 and y= 3#.
But to be sure, always double-check your work by replacing your values in the equations to see if they make the equations true.
#-3(-4) - 3(3) =3#
#12 - 9 = 3 -># true
#3 = -5(-4) - 17#
#3 = 20 - 17 -># true
The values of #x# and #y# make the equations true, hence #x=-4# and #y=3#.