how can i solve this equation ?

Question

a/x +b/y = a/2 + b/3

a/x - b/y = a/2 - b/3

Answer 1

Unless I'm missing something, the two sides of each equation are exactly the same, except that on the left side the denominators are x and y, and on the right side, the denominators are 2 and 3.  Therefore at least one solution is x=2 and y=3.

 

Another way to solve them is simply to add the two equations.  The b terms cancel on both sides, which leaves you with 2a/x = 2a/2, and solving that gives x=2.  Similarly subtracting the two equations results in 2b/y = 2b/3, which leads to y=3.  That's the same as above.

 

The only question is whether there are any other solutions.  Since the equations are not linear, they can POSSIBLY intersect at more than one point.  I don't believe there are any other solutions, but I'm not positive about that.

Answer 2

a/x +b/y = a/2 + b/3  --------eqn 1
a/x - b/y = a/2 - b/3   --------eqn 2

 

If you add both the eqns you will  get

a/x +b/y +a/x -b/y =a/2 +b/3+ a/2 -b/3 (cancel out the same terms with opposite sign)

a/x+a/x = a/2 +a/2  

2a/x = 2a/2  

a/x=a/2      

1/x=1/2

x=2

 

now either you put this value oh x in one of the given equation to get the value of y ,or find (eqn 1- eqn2) to find y in more easy way...

 

eqn 1  - eqn 2 will give you 

(a/x +b/3) - (a/x -b/3)= (a/2+b/3)-(a/2-b/3)

a/x+b/3 - a/x +b/3  = a/2 +b/3 -a/2 +b/3  (cancel out the same terms with opposite sign)

b/y+b/y=b/3+b/3

2b/y= 2b/3

b/y=b/3

1/y = 1/3

y=3