Question

The difference of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b? A. 4,1 B. -19,40 B. 20,1 C. 30,9 D. -8,-29

Answer 1

A-b=21
5a-2b=18

We can use substitution here. Take the first equation and solve for A. (Picking this one because it's easy)

a = 21+b

Plugin to the second equation:5(21+b)-2b=18
Simplify: 105 + 5b - 2b = 18
Simplify: 105 + 3b = 18
Subtract both sides: 3b = 18-105
Simplify: 3b = -87
Divide: b = -29

Plug back into the first: a=21+b
a = 21 - 29
a = -8

Option D