SOLUTION: Solve the system of equations 3x + y = 1 -x + 2y = 9 The answer to this problem is a.(1, 4) or b.(-1, 4) Some say a some say b. Can someone tell me which is the corre

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Solve the system of equations 3x + y = 1 -x + 2y = 9 The answer to this problem is a.(1, 4) or b.(-1, 4) Some say a some say b. Can someone tell me which is the corre      Log On


   



Question 347200: Solve the system of equations
3x + y = 1
-x + 2y = 9
The answer to this problem is a.(1, 4) or b.(-1, 4)
Some say a some say b. Can someone tell me which is the correct answer and why?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Some say a some say b.
Are you taking a poll?
There is only 1 right answer.
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You can do it two ways.
Plug the values in and see which one satisfies the equation.
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Although that works, it won't help you next time you don't have an answer to choose from.
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You can solve by elimination or substitution.
Substitution: Use 1 equation to solve for 1 variable then substitute for that variable in the second equation.
1.3x+%2B+y+=+1
2.-x+%2B+2y+=+9
From eq. 2,
x=2y-9
Substitute into eq. 1,
3%282y-9%29%2By=1
6y-27%2By=1
7y=28
highlight%28y=4%29
Then from eq. 2,
x=2%284%29-9
x=8-9
highlight%28x=-1%29
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The other method is elimination.
Manipulate the equations to eliminate one of the variables.
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1.3x+%2B+y+=+1
2.-x+%2B+2y+=+9
Multiply eq. 2 by 3 and add the equations together.
3x%2By-3x%2B6y=1%2B27
7y=28
y=4
Then use either equation to solve for x.
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Isn't that better than guessing?