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Jared J.
Algebra
12 months ago
If we do so we decrease the first number by 18. So,
#10a+b-18=10b+a#
# or, 10a-a+b-10b=18#
# or, 9a-9b=18#
# or, 9 (a-b)=18#
# or, (a-b)=(18/9)#
# or, (a-b)=2#...... (2)
Solving equation (1) and (2)
#a+b=10#... (1)
#a-b=2#... (2)
In equation (2).
#a-b=2#
# or, a=2+b#
Substitute in equation (1).
#a+b=10#
# or, 2+b+b=10#
# or, 2+2b=10#
# or, 2 (1+b)=10#
# or, 1+b=(10/2)#
# or, 1+b=5#
#:.b=5-1=4#
Re substitute in equation (1)
#a+b=10#
# or, a+4=10#
#:.a=10-4=6#
The numbers are #4# and #6#
Logan H. It is basically asking for a value I do not know how to find.
3 Answers By Expert Tutors
Remember that decimal is a positional number system.
Let the digits of the two-digit number be "ab" [this is a*10+b] "reverse the digits in a certain two digit number you decrease its value by 9" means "the sum of it digits is 11" means ---------------- [elimination; add equations] Now, use either equation [eq1] or [eq2] to find the value of b: --------------------------------- [elimination; subtract equations]
Kenneth S. answered • 12/05/17
Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
Suppose the 2-digit number consists of t as the tens position, u as the units position.
Then the value of this number is 10t+u.
If the digits are reversed, a different number is formed & its value must be 10u+t.
Now you have two equations: 10t+u = 10u+t + 9 (because "When you reverse the digits in a certain two digit number you decrease its value by 9").
So you have a system of two equations and two unknowns, which you can solve.