SOLUTION: How do I solve by using a system of two equations in two variables?
The units digit of a two-digit number is 1 less than 3 times the tens digit. If the digits are reversed, the
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Question 141363This question is from textbook Prentice hall algebra 1
: How do I solve by using a system of two equations in two variables?
The units digit of a two-digit number is 1 less than 3 times the tens digit. If the digits are reversed, the new number is 45 more than the original number. Find the number.
This question is from textbook Prentice hall algebra 1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = 10's digit
Let y = units digit
:
The original 2 digit number: (10x + y)
:
Write an equation for each statement:
"The units digit of a two-digit number is 1 less than 3 times the tens digit."
y = 3x - 1
:
"If the digits are reversed, the new number is 45 more than the original number."
10y + x = 45 + 10x + y
:
Find the number.
10y - y = 10x - x + 45
9y = 9x + 45
Simplify divide equation by 9
y = x + 5
;
Using the equation from the 1st statement, substitute (3x-1) for y; find x
3x - 1 = x + 5
3x - x = 5 + 1
2x = 6
x =
x = 3
:
Find y using y = x + 5
y = 3 + 5
y = 8
:
Our original number = 38
:
:
Check solution in statement:
"If the digits are reversed, the new number is 45 more than the original number."
83 = 45 + 38; confirms our solutions
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