Question

Find the values of $(x+y)$ and $(x-y)$without actually solving for $x$ and $y$.

$13x+15y=114and15x+13y=110$

• A. $x+y=9,x-y=-2$
• B. $x+y=8,x-y=-2$
• C. $x+y=3,x-y=-2$
• D. $x+y=1,x-y=-2$

Answer 1

The correct option is B $x+y=8,x-y=-2$

$13x+15y=114$ ...(i)

$15x+13y=110$ ...(ii)

On adding (i) and (ii) , we get

$28x+28y=224$

$\Rightarrow x+y=\frac{224}{28}=8$

On subtracting (i) from (ii) , we get

$2x-2y=-4$

$\Rightarrow x-y=-\frac{4}{2}=-2$.