Multiple choice

Solve the following equations by substitution method. $\dfrac{1}{x} + \dfrac{2}{y} = 9; \dfrac{2}{x} + \dfrac{1}{y} = 12 (x \neq 0, y \neq 0)$

  1. $x = \dfrac{1}{5} , y = \dfrac{1}{2}$
  2. $x = \dfrac{2}{5} , y = \dfrac{1}{2}$
  3. $x = \dfrac{1}{5} , y = \dfrac{-1}{2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u=1/x, v=1/y. u+2v=9, 2u+v=12. Multiply first by 2: 2u+4v=18. Subtract: 3v=6, v=2, y=1/2. u+4=9, u=5, x=1/5.

AI explanation

By letting u equal 1/x and v equal 1/y, the system transforms into u + 2v equals 9 and 2u + v equals 12. Multiplying the first equation by 2 gives 2u + 4v equals 18, and subtracting the second equation from this eliminates u, resulting in 3v equals 6, so v equals 2. Substituting v back into the second equation gives 2u + 2 equals 12, meaning u equals 5. Therefore, x equals 1/5 and y equals 1/2.

Keep practicing — related questions