Question

Find the values of x and y if:
(5x - 3y, y - 3x) = (4, -4)

Answer 1

Two ordered pairs are equal.
⇒ Therefore their first components are equal and their second components too are separately equal.
(5x - 3y, y - 3x) = (4, -4)
5x - 3y = 4 .......(A) and y - 3x = -4 ......(B)
Now multiplying the equation (B) by 3, we get
3y - 9x = -12......(C)
Now adding both the equations (A) and (C) , we get
(5x - 3y) + (3y - 9x) = (4 + (-12))
-4x = -8
x = 2
Putting the value of x in the equation (B), we get
y - 3x = -4
⇒ y = 3x -4
⇒ y = 3(2) -4
⇒ y = 2
Therefore we get,
 x = 2, y = 2