SOLUTION: 2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UKNOWNS The sum of the digits of a two digit number is 14. When the digit are reversed, the resulting numb

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UKNOWNS The sum of the digits of a two digit number is 14. When the digit are reversed, the resulting numb      Log On


   

Question 1122286: 2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UKNOWNS
The sum of the digits of a two digit number is 14. When the digit are reversed, the resulting number is 23 less than two times the original number. What is the number?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) x +y = 14
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2) 10y +x = 2(10x +y) -23
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simplify equation 2
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10y +x = 20x +2y -23
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3) 19x -8y = 23
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solve equation 1 for x and substitute in equation 3
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19(14-y) -8y = 23
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266 -19y -8y = 23
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-27y = -243
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y = 9
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x = 14 -9 = 5
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x = 5 and y = 9 and the number is 59
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check the answer
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95 = 2(59) -23
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95 = 95
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