Question

The sum of two numbers is 66. Their difference is 8. write a system of equations. Use the system to find the numbers.

Answer 1

x + y = 66
x - y = 8
solve second equation for x
x = y + 8
substitute for x in first equation
y+8 +y = 66

2y = 58
y = 29
x - 29 = 8
x = 37
x = 37 and y = 29

Answer 2

Assume that the two numbers are x and y.
We are given that:
1- Their sum is 66, this means that:
x+y = 66 .......> equation I
This can be rewritten as:
x = 66-y ........> equation II
2- Their difference is 8, this means that:
x-y = 8.......> equation III

Substitute with equation II in III to get y as follows:
x-y = 8
66-y-y = 8
66-2y = 8
66-8 = 2y
58 = 2y
y = 29

substitute with y in equation II to get x as follows:
x = 66-y = 66-29 = 37

based on the above calculations, the two numbers are 29 and 37