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?

Answer 1

$a-b=21 \ \ \ |\times (-2) \\ 5a-2b=18 \\ \\ -2a+2b=-42 \\ \underline{5a-2b=18 \ \ \ \ \ \ \ } \\ 5a-2a=18-42 \\ 3a=-24 \ \ \ |\div 3 \\ a=-8 \\ \\ a-b=21 \\ -8-b=21 \ \ \ |+8 \\ -b=29 \ \ \ |\times (-1) \\ b=-29$

a is equal to -8, b is equal to -29.

Answer 2

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

Set up the first equation so that it equals a or b. This method is using substitution to help solve the problem. So, if you add the inverse of a or b.. So let's say..

a-b(+b)=21+b

So, obviously the variables cancel out and you make sure you follow the rule of what you do to one side, you do to the other. Now you're left with

a=21+b

Now plug in this equation above into your second equation, and solve. :)

So,

5(21+b)-2b=18

Distribute
21 x 5 = 105
5 x b = 5b

Now,
105 + 5b -2b=18
105 +3b=18

105-105+3b=18-105
3b=-87
b= -29

Now plug in b into the first (original) equation:

a-(-29)=21

Since 2 negatives equal a positive, then it is written as follows:

a+29=21

Subtract.

21-29=-8

a=-8

So to check you answer plug in the values of the first equation of a-b=21. So, (-8)-(-29)=21. Again 2 negatives equal a positive so it become -8+29. So this equals a positive 21. :) Best wishes!