Question

If $ 2x+3y=14 $ and $ 2x-3y=2 $ , then find the value of xy.

Answer 1

Hint: Start by solving the system of two equations given in the question to get the values of x and y. For solving the equations use the method of elimination. Add both the equations to eliminate y and solve the expression you get to get the value of x. Put the value of x in one of the parent equations to get the value of y. Once you get x and y, multiply the values to get the value of xy.

Complete step-by-step answer:
Let us start the solution to the above question by solving the equations given in the question.
 $ 2x+3y=14............(i) $
 $ 2x-3y=2...........(ii) $
Now, to eliminate y, we will add equation (i) and equation (ii). On doing so, we get
 $ 2x+3y+2x-3y=14+2 $
 $ \Rightarrow 4x=16 $
Now, we will divide both sides of the equation by 4. On doing so, we get.
 $ \Rightarrow x=\dfrac{16}{4}=4 $
Now, we will put the value of x in equation (i). On doing so, we get
 $ 2x+3y=14 $
 $ \Rightarrow 2\times 4+3y=14 $
 $ \Rightarrow 3y=14-8=6 $
Now, if we divide both sides of the equation by 3, we get
 $ \Rightarrow y=\dfrac{6}{3}=2 $
So, the values of x and y are 4 and 2, respectively. Now, let us find the value of xy using these values.
 $ xy=4\times 2=8 $
Hence, we can conclude that the answer to the above question is 8.

Note: You could have solved the above question by squaring both sides of both the equations and subtracting one from the other and that would have directly given you the value of xy and you could have skipped the steps of finding the values of x and y.