How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #y = -x - 4# and #y = x + 2#?

1 Answer
May 29, 2017

Answer:

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for #y# we can substitute #(-x - 4)# from #y# in the second equation and solve for #x#:

#y = x + 2# becomes:

#-x - 4 = x + 2#

#color(red)(x) - x - 4 - color(blue)(2) = color(red)(x) + x + 2 - color(blue)(2)#

#0 - 6 = color(red)(1x) + 1x + 0#

#-6 = 2x#

#-6/color(red)(2) = (2x)/color(red)(2)#

#-3 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))#

#-3 = x#

#x = -3#

Step 2) Substitute #-3# for #x# in the first equation and calculate #y#:

#y = -x - 4# becomes:

#y = -(-3) - 4#

#y = 3 - 4#

#y = -1#

The solution is: #x = -3# and #y = -1# or #(-3, -1)#