Question

solve the following pair of equations​

Answer 1

Answer:

10(1÷x+y) + 2(1÷x-y) =4--------eq 1

15(1÷x+y) - 3(1÷x-y) =-2-------eq 2

Replacing (1÷x+y) and (1÷x-y) by m and n in both the equation.

we get,

10m+2n=4-------- eq 3

15m-3n=-2-------eq 4

multiply equation 3 by 3 and equation by -2.

30m+6n=12------- eq 5

-30m+6n=4-------eq 6

subtracting equation 6 from 5

30m+6n=12

+30m-6n=-4

__________

60m=8

m=8÷60

m=2÷15

substituting value of m equation 3.

10m+2n=4

10(2÷15)+2n=4

(20÷15)+2n=4

(4÷3)+2n=4

2n=4×3÷4

2n=3

n=3÷2

solve this equation we get m = 2÷15 , n= 3÷2.

But,m=(1÷x+y) and n=(1÷x-y)

2÷15=1÷x+y 3÷2=(1÷x-y)

cross multiplication

2(x+y)=15 3(x-y)=2

2x+2y=15---- eq 7 3x-3y=2----- eq 8

multiply equation 7 by 3 and equation 8 by 2

6x+6y=45----eq 9 6x-6y=4-----eq10

adding equation 9 and 10

6x+6y=45

+6x-6y= 4

_________

12x=49

x=49÷12

putting the value of x in equation 7

2x+2y=15

2(49÷12)+2y=15

49÷6+2y=15

2y=15-49÷6

2y=90-49÷6

2y=39÷6

2y=13÷2

y=13÷2÷2

y=13÷2×1÷2

y=13÷4

solution of the given linear equation is (x,y)=(49÷12,13÷4)