After reversing the digits, the number increases by 36.
We will create a system of linear equations and solve it to help us find the original number. If we let x be the tens digit of our number and y be the ones digit, we can write an equation that represents the first property.
x+ y=8
Now let's move on to the second property of our unknown number. It is a little more complicated, so we will begin by recalling a property about two digit-numbers, using the number 32 as an example.
As we can see, every two-digit number consists of one digit representing the tens and the other representing the ones. We can write every two-digit number as a sum of the tens digit multiplied by 10 and the ones digit. Let's write our unknown number in this format.
The two-digit number x y=10* x+ y
Now on to the second part of the second property. From the exercise, we know that after reversing the digits in our unknown two-digit number x y, its value increases by 36. This means that if y were the tens digit and x the ones digit, the number would be greater by 36. Let's try to write this property as an equation.
10* y+ x=10* x+ y + 36
Now we are ready to create a system of linear equations!
x+y=8 & (I) 10y+x=10x+y+36 & (II)
We can use the Substitution Method to solve our system. First, let's isolate x on one side of the equality in Equation (I).
x+y=8 ⇔ x=8-y
The next step in the Substitution Method is to substitute the value of x we found in one equation into to other equation and solve it for y. Let's do it!
Now that we have a value for y, we can substitute its value for y in either equation and solve for x. Let's substitute 6 for y in Equation (I) for simplicity.
