Find two numbers a and b whose sum a + b is 5 and whose difference a − b is 5.

Answer 1

System of Equations Problem as shown below.

Two numbers whose sum is 5 means the equation is x + y = 5

Two numbers whose difference is 5 means the equation is x - y = 5

System:

x + y = 5

x - y = 5

You should use elimination to get rid of the y variable.

x + y = 5

+ (x - y = 5)

2x = 10

Solve for x by dividing by 2.

x = 5

Substitute x = 5 into the equation x + y = 5.

5 + y = 5

y = 0.

Answer: 5 and 0.