Question

16. Solve the following system of equations in x and y
ax + by = 1
b.x + ay =
(a+b)
2ab
1 or, bx + ay = (3)​

Answer 1

ax+by=1

b.x+ay=

(a+b)

2ab

1 or , bx+ay=(3)

Answer 2

Expert Answer:

ax + by = 1 ------ (1)

bx + ay = [(a + b)^2/(a^2 - b^2)] - 1 ------ (2)

From (2),

bx + ay = [(a + b)(a + b)/(a + b)(a - b)] - 1

bx + ay = [(a + b)/(a - b)] - 1 ------ (3)

Adding (1) and (3),

(x + y)(a + b) = (a + b)/(a - b)

x + y = 1/(a - b)

x = [1/(a - b)] - y ----- (4)

From (4) and (1),

ax + by = 1

[a/(a - b)] - ay + by = 1

y(b - a) = 1 - [a/(a - b)]

y(b - a) = -b/(a - b)

y = b/[(b - a)^2] = [b/(a - b)^2] ----- (5)

From (5) and (4),

x = [1/(a - b)] - y

x = [1/(a - b)] - [b/(a - b)^2]

x = [1/(a - b)] - [b/(a - b)^2]

x = (a - 2b)/(a - b)^2

x = (a - 2b)/(a - b)^2, y = b/(a - b)^2

In case you're wondering, (b - a)^2 = (a - b)^2