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Question 95: the sum of two numbers in 9. the difference between five times of the first and four times of the second is 9. what are that numbers?
Answer by terrtwo(10)   (Show Source):
You can put this solution on YOUR website! translates Algebraically into:
x + y = 9 AND 5x - 4y = 9.
Solving the first eqaution for y, y = 9 - x.
Then substituting the first equation into the second:
5x - 4(9 - x) = 9 --> 5x - 36 + 4x = 9 --> 9x - 36 = 9.
Adding 36 to both sides --> 9x -36 + 36 = 9 + 36 --> 9x = 45.
Divide both sides by 9 --> 9x/9 = 45/9 --> x = 5.
Not finished yet since we still must go back to find y by subsititing the known value of x into either of the orginal equations --> 5 + y = 9
Substact 5 from both sides --> 5 + y - 5 = 9 - 5 --> y = 4
Therefore x = 5, y = 4
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