Algebra 2 word problem help ?

naomi-cook_60976638678e6

The tens digit of a two-digit positive integer is 2 more than three times the ones digit .if the digits are interchanged ,the new number is 13 less than half the given number find the given integer ( hint : let x =tens place digit and y=ones -place digit then 10x + y is the number)

ron-w

The first sentence translates almost verbatim to

x = 2+ 3y

If 10x + y is the original number, then 10y + x is the number resulting from interchanging the digits. The second sentence says

10y + x = ½(10x + y) - 13

Multiply both sides of this by 2 to get rid of the fraction:

20y + 2x = 10x + y - 26

Simplify:

19y = 8x - 26

So you have the system

x = 2 + 3y

19y = 8x - 26

Use the first equation to substitute for x in the second equation:

19y = 8(2 + 3y) - 26

19y = 16 + 24y - 26

19y = 24y - 10

10 = 5y

2 = y

x = 2 + 3y = 8

So the original number is 82.