SOLUTION: Solve the equations by graphing. Then classify the system. x+y=9 x-y=5 What is the solution to the system? ________ Is the system consistent or inconsistent? ___ Ar

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the equations by graphing. Then classify the system. x+y=9 x-y=5 What is the solution to the system? ________ Is the system consistent or inconsistent? ___ Ar      Log On


   

Question 161077: Solve the equations by graphing. Then classify the system.
x+y=9
x-y=5
What is the solution to the system? ________
Is the system consistent or inconsistent? ___
Are the equations dependent or independent? ______
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:


system%28x%2By=9%2Cx-y=5%29


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


Let's graph the first equation:


x%2By=9 Start with the first equation.


y=9-x Subtract x from both sides.


y=-x%2B9 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=-x%2B9.


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Now let's graph the second equation:


x-y=5 Start with the second equation.


-y=5-x Subtract x from both sides.


y=%285-x%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=x-5 Rearrange the terms and simplify.


Now let's graph the equation:


Graph of y=x-5.


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Now let's graph the two equations together:


Graph of y=-x%2B9 (red). Graph of y=x-5 (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.