Question 521530
let x = the 10's digit
Let y = the units
then
10x+y = "certain number"
:
Write an equation for each statement:
:
"Three times the ten digit of a certain two-digit number is two more than four times the units digit."
3x = 4y + 2
3x - 4y = 2
:
" The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits."
(10x+y) - (10y+x) = 2(x+y) - 2
10x + y - 10y - x = 2x + 2y -3
9x - 9y = 2x + 2y -  2
9x - 2x - 9y - 2y = -2
7x - 11y = -2
:
Use these two simplified equations for elimination
Mult the 1st by 7, mult the 2nd by 3
21x - 28y = 14
21x - 33y = -6
----------------subtraction eliminates x, find y
0 + 5y = 20
y = 20/5
y = 4
:
Use 3x = 4y +2, replace y with 4
3x = 4(4) + 2
3x = 18
x = 18/3
x = 6,
then
64 is the number
:
:
Check this in the statement:
" The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits."
64 - 46 = 2(6+4) - 2
 18 = 2(10) - 2