Question

ax+by-c=0,bx+ay-(1+c)=0 find x and y ​

Answer 1

Answer:

x = c/(a+b)  - b/(a²-b²)

y = c/(a+b) + a/(a² - b²)

Step-by-step explanation:

ax + by - c = 0

=> ax + by = c  - eq 1

bx + ay -(1+c) = 0

=> bx + ay = c + 1  - eq 2

Lets multiply eq 1 with a & Eq 2 with b and subtracting 2nd from 1

=> a²x  + aby - b²x - bay = ac - bc - b

=>  a²x  - b²x = ac - bc - b

=> x(a²-b²) = ac - bc - b

=> x = c(a-b)/(a²-b²)    - b/(a²-b²)

=> x = c/(a+b)  - b/(a²-b²)

Now to find b multiply eq 1 with b & Eq 2 with a and subtracting 1 from 2nd

=> abx + a²y - bax - b²y =  ac + a - bc

=> y(a² - b²) = c(a-b) + a

=> y = c/(a+b) + a/(a² - b²)