If $x + y = 6$ and $3 x - y = 4$ , find the value of $x - y$ .

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Solution

The correct option is A $- 1$
Given : $x + y = 6$ and $3 x - y = 4$
$\Rightarrow x + y = 6$ ...(1)
$\Rightarrow 3 x - y = 4$ ...(2)
Multiply equation (1) by 3 and (2) by 1
$\Rightarrow 3 (x + y) = 18$ and $1 (3 x - y) = 4$
$\Rightarrow 3 x + 3 y = 18$ ..(a)
and $3 x - y = 4$ ..(b)
Subsituting (a) - (b)
$\Rightarrow y = \frac{7}{2}$
and now the value of x is taken out by :
$\Rightarrow x + y = 6$
$\Rightarrow x + \frac{7}{2} = 6$
$\Rightarrow x = 6 - \frac{7}{2}$
$\Rightarrow x = \frac{5}{2}$
Now the value of x- y is:
$\Rightarrow x - y = \frac{5}{2} - \frac{7}{2}$
$\Rightarrow x - y = - 1$
The value of x- y is $- 1$

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If x+y=6 and 3x−y=4, find the value of x−y.

If $x + y = 6$ and $3 x - y = 4$ , find the value of $x - y$ .