SOLUTION: Solve the system of equations by graphing x-y=2 x+y=6

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Question 198374: Solve the system of equations by graphing
x-y=2
x+y=6
Found 2 solutions by arallie, jim_thompson5910:
Answer by arallie(162)   (Show Source): You can put this solution on YOUR website!

(4,2)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:





In order to graph these equations, we must solve for y first.


Let's graph the first equation:


Start with the first equation.


Subtract from both sides.


Divide both sides by to isolate .


Rearrange the terms and simplify.


Now let's graph the equation:


Graph of .


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Now let's graph the second equation:


Start with the second equation.


Subtract from both sides.


Rearrange the terms and simplify.


Now let's graph the equation:


Graph of .


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Now let's graph the two equations together:


Graph of (red). Graph of (green)


From the graph, we can see that the two lines intersect at the point . So the solution to the system of equations is . This tells us that the system of equations is consistent and independent.
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