find x and y :10/x+y + 2/x-y=4 and 15/x+y - 5/x-y=-2

Question

it is of pairs of linear equation in two variable class 10 ncert ch-3 ex3.6 (7)

Answer 1

10/(x+y)+2/(x-y)=4, 15/(x+y)-5/(x-y)=-2.

There are several ways of solving: try this one: let X=1/(x+y) and Y=1/(x-y):

10X+2Y=4, which reduces to 5X+Y=2; 15X-5Y=-2, substituting the new variables. We arrive at simultaneous linear equations.

So, multiplying the first equation by 3, 15X+3Y=6 and 15X-5Y=-2, so subtracting these gives 8Y=8, making Y=1.

Since 5X=2-Y=1, X=1/5.

Now we can substitute back for X and Y:

x+y=5 and x-y=1; so, adding, 2x=6 and x=3, therefore y=2.

CHECK: 10/5+2/1=4 OK; 15/5-5/1=3-5=-2 OK.