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Question 928005: the sum of two numbers is 2 and the sum of 5 and their product is also 2. using m to denote the larger number and n to denote the smaller: 1, form a pair of equation in m and, n, and solve them to find the two numbers
Found 2 solutions by stanbon, 428225:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the sum of two numbers is 2 and the sum of 5 and their product is also 2. using m to denote the larger number and n to denote the smaller: 1, form a pair of equation in m and, n, and solve them to find the two numbers
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Equations:
m + n = 2
5 + mn = 2
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substitute for "m" and solve for "n"::
5 + (2-n)n = 2
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2n-n^2 = -3
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n^2 - 2n -3 = 0
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Factor:
(n-3)(n+1) = 0
n = 3 or n = -1
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If n = 3, m = 2-3 = -1
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If n = -1, m= 2+1 = 3
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Cheers,
Stan H.
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Answer by 428225(90)  (Show Source):
You can put this solution on YOUR website! m+n=2 (equation 1)
mn+5=2 (equation 2)
Rearrange equation 1 to get:
m=2-n
Then substitute m=2-n into equation 2
n(2-n)+5=2
2n-n^2+5=2 (subtract by 2)
-n^2+2n+3=0 (multiply by -1)
n^2-2n-3=0
(n-3)(n+1)=0
Therefore n either = -1 OR 3
substitute n=-1 into equation 1 and you get m=3
Then substitute n=3 into equation 1 and get m=-1
THEREFORE, m=3 and n=-1 because m has to be the larger number and n is only the larger number when n=-1
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