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

C. 

20, 1

D. 

30, 9

E. 

-8, -29

Answer 1

Answer:

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