Question

2x+3y=15,2/x+3/y=1/15 find x & y

Answer 1

2x + 3y = 15

(2/x) + (3/y) = 1/15

Our first step is to eliminate one of the variables. In the first equation, by moving 2x to the right:

3y = 15 - 2x

Simplifying by dividing by three:

y = 5 - (2/3)x

Now substitute this value into the second equation:

(2/x) + 3/(2x/3) = 1/15

2/x + 9/2x = 1/15

Multiplying everything by x:

2 + 9/2 = x/15

Solve for x by multiplying the equation by 15:

30 + 67.5 = x

97.5 = x

Substitute this value into the first or second equation to obtain the value for y. 

Answer 2

2x+3y=15,2/x+3/y=1/15 find x & y
Solution:
           2 x+3y = 15
           2x = 15 - 3y
       or x = (15 -3y ) /2  ............ (1)
         2/x+3/y = 1/15
         By Cross Multiplication , we get
         2y +3x /xy =1/15
         2y+3x =xy/15
         15(2y +3x) = xy
          30y+45x = xy ........... (2)
            Substitute 1 in 2 , we get
                 30y + 45 (15 -3y)/2 = (15 -3y)/2*y
                 30y +(45*15  - 45*3y)/2 = (15 *y - 3y*y) /2
Multiplying by 2 on b/s , we get
                 2*30y + (45*15 - 45*3y) = 15y - 3y²
                 60y +675 - 45y =15y -3y²
                 60y +675 -45y -15y +3y²=0
                 3y²+60y-45y-15y +675 =0
                 3y² +675 =0
                 3y² = -675
                   y² = -675/3
                   y²= - 225
                   or y= 15
substitute y =15 in 1 ,we get
                   x=(15 -3*15 )/2
                     =(15 - 45 )/2
                     =-30/2
                     x=-15
hence x=-15 and y = 15
Hope this helps you!!!!