Final answer:
To solve the system of equations formed by the statement, one number is 8 more than twice the other, and their sum is 20, we can use substitution. By substituting the value of x from one equation into the other, we can solve for the values of x and y. The solution is x = 24 and y = 4.
Step-by-step explanation:
To solve this system of equations, let's assign variables to the two numbers. Let's call the first number x and the second number y.
From the given information, we have two equations:
- x = 2y + 8
- x + y = 20
Now we can solve this system of equations using substitution or elimination. Let's use substitution:
- Substitute the value of x from the first equation into the second equation:
- (2y + 8) + y = 20
- Combine like terms: 3y + 8 = 20
- Subtract 8 from both sides: 3y = 12
- Divide both sides by 3: y = 4
- Substitute the value of y back into the first equation to solve for x:
- x = 2(4) + 8
- Perform the calculations: x = 16 + 8
- x = 24
Therefore, the two numbers that satisfy the given conditions are x = 24 and y = 4.