Question

one number is equal to two times a second number. two times the first number plus two times the second number is 24. if you let x stand for the first number and y for the second, what are the two numbers? a. x = 8, y = 4 b. x = 24, y = 12 c. x = 12, y = 6 d. x = –24, y = –12

Answer 1

`\left\{\begin{array}{ccc}x=2y\\2x+2y=24&|divide\ both\ sides\ by\ 2\end{array}\right\\\left\{\begin{array}{ccc}x=2y\\x+y=12\end{array}\right\\\\subtitute\ x=2y\ to\ the\ x+y=12\\\\2y+y=12\\3y=12\ \ \ |divide\ both\ sides\ by\ 3\\\boxed{y=4}\\\\x=2y\to x=2\cdot4\\\boxed{x=8}\\\\Answer:\fbox{a.}`