SOLUTION: A certain two-digit number has a value that is 2 more than 6 times the sum of its digits. The tens digit is 1 more than the units digit. Find the number by using linear sytems.

Question 262876: A certain two-digit number has a value that is 2 more than 6 times the sum of its digits. The tens digit is 1 more than the units digit. Find the number by using linear sytems.
Found 2 solutions by mananth, ankor@dixie-net.com:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A certain two-digit number has a value that is 2 more than 6 times the sum of its digits. The tens digit is 1 more than the units digit. Find the number by using linear sytems.
Let the digit in tens place be x
And that in the units place be y
10x+y=6(x+y) +2
X=y+1

10x+y = 6x+6y+2
4x-5y=2 -------------1
x-y=1 ----------------2
multiply eq 2 by 4 and subtract the equations
4x-4y=4
4x-5y=2
Y=2
X=3
The number is 31

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let x = the 10's digit
let y = the units
then 10x + y = the two digit number
:
Write an equation for each statement:
:
"A certain two-digit number has a value that is 2 more than 6 times the sum of its digits."
10x + y = 6(x + y) + 2
10x + y = 6x + 6y + 2
10x - 6x = 6y - y + 2
4x = 5y + 2
:
" The tens digit is 1 more than the units digit."
x = y + 1
:
Using equation 4x = 5y + 2, replace x with (y+1)
4(y+1) = 5y + 2
4y + 4 = 5y + 2
4 - 2 = 5y - 4y
2 = y
then
x = 3
;
32 = "the number"
:
:
Check solution in the statement:
"A certain two-digit number has a value that is 2 more than 6 times the sum of its digits. "
32 = 6(3+2) + 2; confirms our solution
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