Belajar Matematika

Problem:
1. If 2x + y = 13 and x + 2y = 11, what is the value of x + y?

2. Determine the units digit of the integer equal to 9 + 9² + 9³ + 9⁴.

(The units digit of an integer is its rightmost digit. For example, the units digit of the integer 1234 is 4.)

Answer ?

Solution 1

Adding the two equations gives (2x + y) + (x + 2y) = 13 + 11 or 3x + 3y = 24.

Thus, x + y = 1/3(24) = 8.

Solution 2
We note that 9 + 9² + 9³+ 9⁴ = 9(1 + 9¹) + 9³(1 + 9¹) = (9 + 9³)(1 + 9) = 10(9 + 9³).

Therefore, 9 + 9² + 9³ + 9⁴ is an integer that is divisible by 10, so its units digit is 0.