How do you solve the system of equations: -3x-3y=3 and y=-5x-17?

1 Answer

Answer:

When solved by substitution:

#x= -4#
#y= 3#

Explanation:

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#.