Question

Find the values of the $x+y$ and $x-y$ from the examples given below without solving for x and y

$5x+7y=17;7x+5y=19$

• A. $-3$, $-1$
• B. $3$, $1$
• C. $1$, $3$
• D. $-1$, $3$

Answer 1

Answer: (B)

$3$, $1$

$\text{The given equations are}$
$5x+7y=17$ ...(i)
$7x+5y=19$ ...(ii)

$\text{On adding (i) and (ii), we get}$

$12x+12y=36\Rightarrow x+y=3$

$\text{On subtracting (i) from (ii), we get}$

$2x-2y=2\Rightarrow x-y=1$

$\therefore x+y=3andx-y=1$