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

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Answer 1 · 2017-07-03T06:24:13

$x = 9, y = 3$ $x = 9, y = 3$

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

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

$\Rightarrow x + y = 12$ $Rightarrow x + y = 12$

$\Rightarrow y = 12 - x$ $Rightarrow y = 12 - x$

$and$ $and$

$\Rightarrow x - y = 6$ $Rightarrow x - y = 6$

$\Rightarrow y = x - 6$ $Rightarrow y = x - 6$

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

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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 $x = 9$ $x = 9$ and $y = 3$ $y = 3$ .

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