Question

Solve the system of equations formed by the statement "One number is 8 more than twice the other, and their sum is 20.

Answer 1

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:

1. x = 2y + 8
2. x + y = 20

Now we can solve this system of equations using substitution or elimination. Let's use substitution:

1. Substitute the value of x from the first equation into the second equation:
2. (2y + 8) + y = 20
3. Combine like terms: 3y + 8 = 20
4. Subtract 8 from both sides: 3y = 12
5. Divide both sides by 3: y = 4
6. Substitute the value of y back into the first equation to solve for x:
7. x = 2(4) + 8
8. Perform the calculations: x = 16 + 8
9. x = 24

Therefore, the two numbers that satisfy the given conditions are x = 24 and y = 4.