MathematicsFind the values of (x+y) and (x-y) without actually solving for x and y. 13x+15y=114, 15x+13y=110.

Find the values of $(x + y)$ and $(x - y)$ without actually solving for $x$ and $y$ . $13 x + 15 y = 114, 15 x + 13 y = 110$ .

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

Solution:

Given solutions are,

13 x + 15 y = 114

...(1)

15 x + 13 y = 110

...(2)
On adding equations (1) and (2), we get,
⇒

28 x + 28 y = 224

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

On subtracting (1) from (2), we get,
⇒

2 x - 2 y = - 4

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

⇒

x - y = - 2

Hence, the correct option is 2.

Find the values of $(x + y)$ and $(x - y)$ without actually solving for $x$ and $y$ . $13 x + 15 y = 114, 15 x + 13 y = 110$ .

Solution:

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