Answer to Question #110435 in Discrete Mathematics for hassan

Question

If x, y are real numbers such that ordered pairs (x + y, x -y) and (2x + 3y, 3x - 2y) are equal, then (x, y) is equal to

Answer 1

Given, the ordered pairs $(x + y, x - y)$ and $(2x + 3y, 3x - 2y)$ are equal. Since, two ordered pairs are equal if and only if corresponding coordinates are equal, we get $x+y=2x+3y$ and $x-y=3x-2y$ . That is $-x-2y = 0$ and $-2x + y = 0$. Solving the two equations, we get $x = 0$ and $y = 0$ . Hence the ordered pair $(x,y) = (0,0)$.