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

Question

3 years ago

14

?
A. 4,1
B. -19,40
C. 20,1
D. 30,9
E. -8,-29

1 answer:

bixtya [17] · Answer 1 · 2022-06-11T23:44:43+03:00

Answer:

The solution set is (-8, -29) (Answer E)

Step-by-step explanation:

Changing the given info into equations, we obtain:

a - b = 21 and

5a - 2b = 18

Let's use elimination by addition/subtraction. Multiply the first equation by -5 to obtain

-5a + 5b = -105

and then add this result to the second equation:

-5a + 5b = -105

5a - 2b = 18

-------------------------

3b = - 87

Dividing both sides by 3 yields:

b = -87/3 = -29

Now substitute -29 for b in a - b = 21

a - (-29) = 21, or a + 29 = 21. Then a = -8.

The solution set is (-8, -29) (Answer E)