How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x+y = 12# and #x-y = 6#?

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Answer 1 · 2017-07-03T06:24:13

#x = 9, y = 3#

We have: #x + y = 12# and #x - y = 6#

First, let's solve both equations for #y#:

#Rightarrow x + y = 12#

#Rightarrow y = 12 - x#

#and#

#Rightarrow x - y = 6#

#Rightarrow y = x - 6#

Then, let's graph both of these rearranged equations:

enter image source here
Image from Desmos

As you can see from the graph, the system is consistent because there is a point of intersection, i.e. a solution to the system of equations.

The solutions to the system of equations are #x = 9# and #y = 3#.