SOLUTION: The sum of the digits of a certain two-digit number is 7.Reversing the digits increases the number by 9.What is the number? Write and solve linear systems of equation for these pro
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Question 262900: The sum of the digits of a certain two-digit number is 7.Reversing the digits increases the number by 9.What is the number? Write and solve linear systems of equation for these problems. 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:
:
The sum of the digits of a certain two-digit number is 7.
x + y = 7
:
reversing the digits increases the number by 9.
10y + x = 10x + y + 9
10y - y = 10x - x + 9
9y = 9x + 9
Simplify, divide by 9
y = x + 1
We can arrange it like this, add to the 1st equation
-x + y = 1
+x + y = 7
--------------addition eliminates x find y
2y = 8
y = 4
then, obviously
x = 3
:
34 is the number
;
:
Check solution in the statement:
reversing the digits increases the number by 9.
43 = 34 + 9
