(i) ax + by=c
bx + ay = 1 + c
Answers
Answer:
Step-by-step explanation:
ax + by = c . . . . . . . . .(1)
bx + ay = 1 + c . . . . . . . . .(2)
Add (1) and (2)
(a+b) x + (a +b) y = 1 + 2c
∴ x + y = . . . . . . . . . .(3)
Substract (2) from (1)
(a -b) x - (a -b) y = -1
∴ x - y = . . . . . . . . .(4)
Add (3) and (4)
2x = -
=
=
x =
From (1)
y = -
=
=
=
Step-by-step explanation:
Given :
ax + by = c----(i)
bx + ay = 1 + c ---(ii)
To solve :
For x and y.
Solution :
multiply equation (i) by a and equation (ii) by b and subtracting (ii) from (i) we get,
a^2 x + aby - b^2 x - bay = ac - b - bc
=> x ( a^ - b^2 ) = c ( a - b) - b
=> x = [ c (a - b) - b ]/ (a^2 - b^2)]
Similarly, multiply equation (i) by b and equation (ii) by a and subtracting (ii) from (i) we get,
abx + b^2 y - abx - a^2 y = bc - a - ac
=> y (b^2 - a^2) = c(b - a) - a
=> y = [ c(b - a) - a]/(b^2 - a^2)