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

C.

20, 1

D.

30, 9

E.

-8, - 29

E. - 8, - 29

Step-by-step explanation:

a-b=21

5a - 2b = 18

Take the first equation and solve for a by adding b to each side

a-b=21

a-b+b=21+b

a = 21+b

Now substitute a=21+b into the second equation

5a - 2b = 18

5 (21+b) - 2b = 18

Distribute the 5

105 + 5b-2b = 18

Combine like terms

105 + 3b = 18

Subtract 105 from each side

105-105 + 3b = 18-105

3b = - 87

Divide each side by 3

3b/3 = -87/3

b = - 29

if b = - 29, we can substitute it into a = 21+b

a = 21-29

a = - 8