Question

solve for 2/x+3/y=2 and 1/x -1/2y=1/3.
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Answer 1

Answer:

x=2 y=3

Explanation:

2/x+3/y=2. =2y+3x=2xy. (l.c.m). ----1

1/x-1/2y=1/3. = 2y-x=2xy/3 (l.c.m)-----2

using value of 2xy from (1) in (2)

2y-x =2y/3 +3x/3

2y-2y/3 =3x/3 +x

using lcm

6y/3-2y/3 =2x

4y/3 =2x. ----------(3)

using value of x from 3 in 1

2y +3(4y/6) = y×4y/3

2y +12y/6 =(4y^2)/3

taking l.c.m

12y/6 +12y/6 =(4y^2)/3

24y/6=(4y^2)/3

4y×4 = 4y^2

12y = 4y^2

12=4y

y=3

using value of y in (3)

12/3=2x

4=2x

x=2

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