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 |\cdot(-2)\\ 5a-2b=18\\\\ -2a+2b=-42\\ \underline{5a-2b=18}\\ 3a=-24\\ a=-8\\\\ -8-b=21\\ b=-29`

Answer 2

`a-b=21 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |* (-2) \\ 5a-2b=18 \\ \\ -2a+2b=-42 \\ \underline{5a-2b=18 \ \ \ \ \ \ \ } \\ 5a-2a=18-42 \\ 3a=-24 \\ a=(-24)/(3) \\ a=-8 \\ \\ a-b=21 \\ -8-b=21 \\ -b=21+8 \\ -b=29 \\ b=-29`

a=-8 and b=-29.