Question 156579: Give ordered pair (m,n) of numbers that satisfy the equation
4m-n=9
how do I figure this out...thanks for your help!
Found 2 solutions by Fombitz, Electrified_Levi:
Answer by Fombitz(32388)   (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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Give ordered pair (m,n) of numbers that satisfy the equation
how do I figure this out...thanks for your help!
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(m,n) is the same as (x,y)
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All you do is, pick any number for "m"(x)(usually small numbers), and put in equation
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We will use "3" for "m",(replace "m" with "3" in equation, then solve for "n"(y))
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=  , multiplying we get, 
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To solve "n", we will move (-n) over to right to make it positive
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=  =  Rearranging we get 
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Now all we need to do to get "n" is move "9" over to the left side
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=  =  = 
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We found "n", "n" = 3
We used "3" for "m", "m" = 3
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"m"(x) = 3
"n"(y) = 3
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We can check by replacing "m" and "n" with our numbers, in the equation
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=  =  =  (True)
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We found the ordered pair, (m,n), our ordered pair is (3,3)
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Let's get another ordered pair
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(you can replace "m" with any number) we will use "1" for "m", (replace "m" with "1" in equation)
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=  Multiplying we get 
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Moving (-n) to the right
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=  =  , Rearranging it equals 
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We will move "9" over to the left to find "n"
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=  =  = 
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"n" = (-5)
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"m" = 1
"n" = (-5)
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To check we will replace "m" and "n" in our equation
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=  =  , double negative, which makes positive,  =  (True)
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We found another ordered pair (m,n), our second ordered pair is (1, -5)
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If you want you can also pick any number for "n", let's get another ordered pair, by picking any number for "n"
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Let's use "7" for "n"(replace "n" with "7" in equation)
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=  =  , since "m" is already positive, we will move (-7) to the right
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=  =  , now all we need to do is divide each side by (4) to get "m"
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=  =  = 
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"m" = 4
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"m" = 4
"n" = 7
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We check it by replacing the letters( "m" and "n") with the numbers in the equation
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=  =  =  = ( True)
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We found a third ordered pair that satisfies the equation, , (m,n), our third ordered pair = (4,7)
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The ordered pairs (3,3) , (1,-5), (4,7) satisfy the equation, ,can you find any more?
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Hope I helped, Levi
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