Answer:
The original two-digit number is 34.
Explanation:
Let's represent the original two-digit number as "xy", where "x" is the tens digit and "y" is the ones digit.
We have the following equation:
x + y = 7 ---(Equation 1)
The second equation states that reversing the digits increases the number by 9. This can be expressed as:
10y + x = 10x + y + 9 ---(Equation 2)
Now, we can solve this system of equations to find the values of "x" and "y".
Multiplying Equation 1 by 10, we get:
10x + 10y = 70
Subtracting Equation 1 from Equation 2, we have:
10y + x - (10x + y) = 9
Simplifying:
9y - 9x = 9
Now, let's divide both sides of the equation by 9:
y - x = 1 ---(Equation 3)
Next, let's add Equation 1 and Equation 3:
x + y + y - x = 7 + 1
Simplifying:
2y = 8
Dividing both sides by 2:
y = 4
Substituting the value of "y" back into Equation 1:
x + 4 = 7
Subtracting 4 from both sides:
x = 3
= 34