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asambeis [7]
3 years ago
10

Let x and y represent the tens digit and ones digit of a two digit number, respectively. The sum of the digirs of a two digit nu

mbet is 9. If the digits are reversed, the new number is 27 more than the original number. What is the original number? *Write a system of equations *solve the systems of equations
Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0

Answer:

The Original Number is 36

Step-by-step explanation:

Given:

y is the number in units place

x is the number in tens place

Original Number = 10x+y

x+y=9 is equation 1

Now after interchanging the digits

New number = 10y+x

New Number = 27 + Original Number

Substituting Valus in above equation we get.

10y+x=27+10x+y\\10y-y+x-10x=27\\9y-9x=27\\9(y-x)=27\\y-x=\frac{27}{9}\\

y-x=3 let this be equation 2

Adding equation 1 and 2 we get

(x+y=9)+(y-x=3)\\2y=12\\y=\frac{12}{2}\\y= 6\\

Substituting value of y in equation 1 we get

x+y=9\\x+6=9\\x=9-6\\x=3

x=3 and y=6

Original Number = 10x+y=10\times3+6=30+6=36

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