Question

4/x-y+1/x+y=3 2/x-y-3/x+y=5

Answer 1

Answer:

2x−y=3 ------- (1)

4x+y=3 ------ (2)

From equation 1 :

y=2x−3

Substitute the value of y in equation 2 :

4x+y=3

4x+2x−3=3

6x=3+3

X=

6

6

=1

Now, Substitute x=1 in equation 1 :

2x−y=3

2(1)−y=3

2−3=y

Y=−1

Therefore the solution is: x=1 and y=−1

Answer 2

Answer:

$let \: \frac{1}{x - y} = a \: and \: \frac{1}{x + y} = b \\ so \: equations \: can \: be \: rewritten \: as \\ 4a + b = 3.......(1) \\ 2a - 3b = 5.....(2) \\ use \: elimination \: method \\ multiply \: (1) \: by \: 3 \\ 12a + 3b = 9 \\ 2a - 3b = 5 \\ on \: adding \: these \: two \: equations \: we \: get \\ 14a = 14 \\ a = 1.....(3) \\ put \: a = 1 \: in \: eq \: (2) \\ 2 \times 1 - 3b = 5 \\ 3b = - 3 \\ b = - 1 ........(4) \\ \\ now \: a = 1 = > \frac{1}{x - y} = 1 = > x - y = 1 \\ and \: b = - 1 = > \frac{1}{x + y} = - 1 = > x + y = - 1 \\ on \: adding \\ 2x = 0 \: = > x = 0 \\ so \: y \: = - 1$