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

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)

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