Question

HELPP!!
Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers.
The difference between two numbers is 3. The sum of the larger number and twice the smaller number is 21. Find the numbers.

Answer 1

System of equations:

x - y = 3

x + 2y = 21

solving using substitution:

1. isolate one of the variables in one of the equations

x - y = 3

x = 3 + y

2. substitute 3 + y into the other equation

3 + y + 2y = 21

3. simplify

3 + 3y = 21

3y = 18

y = 6

4. substitute 6 back into one of the equations and solve for x

x - 6 = 3

x = 9