Question

Write a system of equations modeling the given conditions. Then solve the system by the
substitution method and find the two numbers.
The sum of two numbers is 94. One number is 36 more than the other. Find the
numbers.

Answer 1

System of equations modeling the given conditions:

x + y = 94

x - y = 36

Solving:

In order to use substitution, you have to isolate one of the variables in either of the equations

Using the second equation and isolating the variable x:

x - y = 36

x = 36 + y

then you can substitute x back into the first equation

36 + y + y = 94

36 + 2y = 94

2y = 58

y = 29

and then substitute 29 for y into either one of the equations

x + 29 = 94

x = 65