Janice is thinking of two numbers. she says that two times the first number plus the second number is 47. in addition, the first number plus three times the second number is 56. find the numbers

Let the numbers be x and y, then
2x + y = 47 . . . (1)
x + 3y = 56 . . . (2)

(2) x 2 => 2x + 6y = 112 . . . (3)

(1) - (3) => -5y = -65 => y = -65/-5 = 13
From (2), x + 3(13) = 56 => x = 56 - 39 = 17

The two numbers are 13 and 17.