The a-variable represents the tens' place digit and the b-variable represents the ones' place digit.
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Practice makes perfect
We are given a way to look at the value of a number so that the a-variable represents the tens' place digit and the b-variable represents the ones' place digit. Let's create equations from each of the given clues.
First Verbal Expression
First Algebraic Expression
Second Verbal Expression
Second Algebraic Expression
The ones' place digit is
b=
The value of the number is
10a+b=
One more than...
...+1
Two more than...
...+2
Twice the tens' place digit
2a
Five times the ones' place digit
5b
b=2a+1
10a+b=5b+2
We now have two equations and two variables. This means we can create and solve a system of equations.
b=2a+1 10a+b=5b+2
Let's start by moving the b terms of the second equation to one side. We will then use the Substitution Method since the first equation already has the b-variable isolated.
