Question

solve the following pair of equation by reducing them to a pair of linear equation.
1/2x+1/3y=2
1/3x+1/2y=13/6
plsssss plsssss answer this question fast plsssss​

Answer 1

1/2x + 1/3y=2.........(1)

1/3x + 1/2y =13/6.........(2)

Let 1/x=u,1/y=v

So,our equation becomes

1/2u+1/3v=2

3u+2v/2x3=2

3u+2v=12..........(3)

1/3u+1/2v=13/6

2u+3v/2X3=13/6

2u+3v=3..........(4)

Our equation are

3u+2v=12.......(3)

3u+3v=13.........(4)

From(3)

3u+2v=12

3u=12-2v

u=12-2v/3

putting value of u in (4)

2u+3v=13

2(12-2v/3)+3v=13

Multiplying both sides by 3

3X2(12-2v/3)+3X3v=3X13

2(12-2v)+9v=39

2u-4v+9v=39

-4v+9v=39-24

5v=15

v=15/5

v=3

putting v=3 in (3)

3u+2v=12

3u+2(3)=12

3u+6=12

3u=12-6

3u=12-6

3u=6

u=6/3=2

u=2

Hence,v=3,u=2

But we have to find x&y

we,know that

u=1/x

2=1/x

x=1/2

v=1/y

3=1/y

y=1/2

So,x=1/2,y=1/3 is the solution of the given equation.

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