Question

10. The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers.

Answer 1

10 and 4.

Explanation:

Let x be the first number.

Let y be the second number.

x + y = 2x - 6

x - y = 4y - 10

x = 4y - 10 + y

x = 5y - 10

(5y - 10) + y = 2(5y - 10) - 6

6y - 10 = 10y - 20 - 6

6y - 10 = 10y - 26

6y - 10y = -26 + 10

-4y = -16

y = 4

x - (4) = 4(4) - 10

x - 4 = 16 - 10

x - 4 = 6

x = 6 + 4

x = 10