## Answers

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.

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!!!!

hence x=-15 and y = 15