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Question 147443: 26) Find values of m and b in the following system so that the solution to the system is (-3,4).
5x+7y=b
mx+y=22
Can someone please show how to solve this problem. I am stuck.
v/r
Found 2 solutions by Nate, Electrified_Levi:
Answer by Nate(3500)   (Show Source):
Answer by Electrified_Levi(103) (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help.
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Find values of m and b in the following system so that the solution to the system is (-3,4).
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5x+7y=b
mx+y=22
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This problem is pretty easy, once you know how to do it.
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5x+7y=b
mx+y=22
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It has told you the value of "x" and "y", which is (-3,4)(x,y).
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In this kind of problem, if it gives you the solution to the system, it refers to "x" and "y" (unless they are replace with other letters of the alphabet, like "r" and "t"), first number in (-3,4) or any solution to a system is "x", second in (-3,4) or any solution to system of equations is "y"
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so "x" is equal to (-3), "y" is equal to 4
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Now all you do is replace "x" and "y".
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5x+7y=b
mx+y=22
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5(-3)+7(4)=b
m(-3)+(4)=22
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Now you have two different problems
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1. 5(-3)+7(4)=b
2. m(-3)+(4)=22
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All you need to do now is solve for "b" and "m".
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1. 5(-3)+7(4)=b
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1. -15+28=b or
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1. b =28 - 15
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1. b = 13
Now let's solve the other equation
2. m(-3)+(4)=22
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2. -3m + 4 = 22
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2. -3m + 4 - 4 = 22 - 4
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2. -3m = 18
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2. 
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2. m = -6
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Now we can replace the letters "b" and "m" with the numbers
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5x+7y=b
mx+y=22
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It becomes
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5x+7y=13
-6x+y=22
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If you want you can check it by replacing the "x" and "y"
Solution = (-3,4), like problem stated
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[5(-3)+7(4)=13]
[-6(-3)+(4)=22]
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[-15+28=13]
[18+4=22]
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[13 = 13]
[22 = 22}
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They both work!
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b = 13
m =(-6)
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Hope this helped, Levi
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