One number is 8 more than another. If the sum of the smaller number and twice the larger number is 46, find the two numbers. Let x = the first number

x = 18 y = 10

Step-by-step explanation:

let the first number be x

let the second number be y

x = y + 8 equation 1

2x + y = 46 equation 2

x is the larger number

y is the smaller number.

Rearrange the equation and add equation 1 to equation 2.

x - y = 8

+ 2x + y = 46

3x + 0 = 54

3x = 54

divide both sides by 3

x = 54/3

x = 18

Substitute x = 18 into equation 1

x = y + 8

18 = y + 8

collect like terms

y = 18-8

y = 10