Question 156579
Hi, Hope I can help,
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Give ordered pair (m,n) of numbers that satisfy the equation 
{{{ 4m-n=9 }}} 
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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{{{ 4m-n=9 }}} = {{{ 4(3)-n=9 }}}, multiplying we get, {{{ 12-n=9 }}}
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To solve "n", we will move (-n) over to right to make it positive
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{{{ 12-n=9 }}} = {{{ 12-n + n = 9 + n }}} = {{{ 12 =9+n }}} Rearranging we get {{{ 12 = n+9 }}}
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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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{{{ 12 = n+9 }}} = {{{ 12 - 9 = n+9 - 9 }}} = {{{ 3 = n }}} = {{{ n = 3 }}}
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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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{{{ 4m-n=9 }}} = {{{ 4(3)-(3)=9 }}} = {{{ 12 - 3 = 9 }}} = {{{ 9 = 9 }}} (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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{{{ 4m-n=9 }}} = {{{ 4(1)-n=9 }}} Multiplying we get {{{ (4)-n=9 }}}
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Moving (-n) to the right
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{{{ (4)-n=9 }}} = {{{ (4)-n + n=9 + n }}} = {{{ 4=9 + n }}}, Rearranging it equals {{{ 4=n + 9 }}}
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We will move "9" over to the left to find "n"
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{{{ 4=n + 9 }}} = {{{ 4 - 9=n + 9 - 9 }}} = {{{ (-5)=n }}} = {{{ n= (-5) }}}
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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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{{{ 4m-n=9 }}} = {{{ 4(1)-(-5)=9 }}} = {{{ 4-(-5)=9 }}}, double negative, which makes positive, {{{ 4 + 5 =9 }}} = {{{ 9=9 }}} (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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{{{ 4m-n=9 }}} = {{{ 4m-(7)=9 }}} = {{{ 4m-7=9 }}}, since "m" is already positive, we will move (-7) to the right
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 {{{ 4m-7=9 }}} = {{{ 4m-7 + 7=9 + 7 }}} = {{{ 4m= 16 }}}, now all we need to do is divide each side by (4) to get "m"
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{{{ 4m= 16 }}} = {{{ 4m/4= 16/4 }}} = {{{ m= 16/4 }}} = {{{ m = 4 }}}
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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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{{{ 4m-n=9 }}} = {{{ 4(4)-(7)=9 }}} = {{{ 4(4)-7=9 }}} = {{{ 16-7=9 }}} = {{{ 9=9 }}} ( True)
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We found a third ordered pair that satisfies the equation, {{{ 4m-n=9 }}}, (m,n), our third ordered pair = (4,7)
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The ordered pairs (3,3) , (1,-5), (4,7) satisfy the equation, {{{ 4m-n=9 }}},can you find any more?
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Hope I helped, Levi