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 numbet 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

Accepted Solution

Answer:The Original Number is 36Step-by-step explanation:Given:y is the number in units placex is the number in tens place Original Number = [tex]10x+y[/tex][tex]x+y=9[/tex] is equation 1Now after interchanging the digits New number = [tex]10y+x[/tex]New Number = 27 + Original NumberSubstituting Valus in above equation we get.[tex]10y+x=27+10x+y\\10y-y+x-10x=27\\9y-9x=27\\9(y-x)=27\\y-x=\frac{27}{9}\\[/tex][tex]y-x=3[/tex] let this be equation 2Adding equation 1 and 2 we get [tex](x+y=9)+(y-x=3)\\2y=12\\y=\frac{12}{2}\\y= 6\\[/tex]Substituting value of y in equation 1 we get[tex]x+y=9\\x+6=9\\x=9-6\\x=3[/tex]x=3 and y=6Original Number = [tex]10x+y=10\times3+6=30+6=36[/tex]