Answer:
The two numbers are 4 and 22.
Step-by-step explanation:
Let the two numbers be x and y. Let y be the smaller number.
x - y = 18
2y + 3x = 74
Solve the first equation for either variable and plug it into the second equation.
Solving for y: x = y + 18
2y + 3(y + 18) = 74
Simplify.
2y + 3y + 54 = 74
5y + 54 = 74
5y = 20
y = 4
Go back and solve for x.
x - y = 18
x - 4 = 18
x = 22
The two numbers are 4 and 22.
Check using both equations.
The difference between 22 and 4 is 18.
Twice the smaller is 8. Three times the larger is 66. The sum of 8 and 66 is 74.
