Question

solve the following pairs of equations by reducing them to a pair of linear equations
5/x+y-2/x-y=-1 , 15/x+y+7/x-y=10 where x≠0,y≠0

Answer 1

Hi friend, Here's the required answer:-

Let 1/ x+y = p and 1/ x-y = q.

Then the pair of linear equations in two variables is-

5p -2q = -1 ---------------(1)
15p +7q= 10. -------------(2)

Now Multiplying the equation (1) by 3.,
15p-6q= -3 ---------------(3)

Now By ELIMINATION METHOD,

Subtracting (3) from (1),

(15p+7q)- (15p-6q)= 10-(-3)
15p +7q-15p+6q = 10+3
13q= 13
q=1

Now putting value of q in (1),
5p-2(1)= -1
5p-2=-1
5p=1
p=1/5

So p= 1/x+y And q= 1/x-y
1/5= 1/x+y. 1= 1/x-y
5= x+y. 1= x-y

Adding both the equation,

x+y+x-y= 5+1
2x= 6
x= 3

Now, x+y=5
3+y=5
y=2

So , x= 3 and y=2.

Hope this helps you....

Answer 2

hope that it will helps you