Question

If $f(2x+3y,2x-7y)=20x,$ then $f(x,y)$ equals

• A. $7x–3y$
• B. $7x+3y$
• C. $3x–7y$
• D. $3x+7y$

Answer 1

The correct option is B

$7x+3y$

Explanation for the correct option:

Step 1. Finding the value of $f(x,y)$ :

Given that $f(2x+3y,2x-7y)=20x,$

Let $2x+3y=X$ ….(i)

$2x–7y=Y$ ….(ii)

Step 2. Subtract equation (ii) from (i), we get

$10y=X-Y$

$\Rightarrow$$y=(X-Y)/10$

Step 3. Put the value of $y$ in equation (i), we get

$2x+3(X-Y)/10=X$

$\Rightarrow$ $\begin{array}{rcl}2x& =& X–(3X/10)+(3Y/10)\\ & =& (7X+3Y)/10\end{array}$

$\Rightarrow$ $x=(7X+3Y)/20$

Now,

$\begin{array}{rcl}f(X,Y)& =& 20x\\ & =& 20(7X+3Y)/20\\ & =& 7X+3Y\end{array}$

$\mathbf{\therefore }\mathit{f}\mathbf{(}\mathit{x}\mathbf{,}\mathbf{}\mathit{y}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathbf{7}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}\mathit{y}$

Hence, Option ‘B’ is Correct.