Question

Solve for x and y
ax + by = a + b
ax (1/a-b - 1/a+b)+ cy(1/b-a - 1/b+a) = 2a/a+b
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Answer 1

The required solution is x = a/b , y = b/c

Step-by-step explanation:

The given equations are

bx + cy = a + b ..... (1)

ax {1/(a - b) - 1/(a + b)} + cy {1/(b - a) - 1/(b + a)} = 2a/(a + b) ..... (2)

or, ax (a + b - a + b)/{(a - b) (a + b)} + cy (b + a - b + a)/{(b - a) (b + a)} = 2a/(a + b)

or, ax (2b)/(a - b) + cy (2a)/(b - a) = 2a

or, bx/(a - b) - cy/(a - b) = 1

or, bx - cy = a - b ..... (2)

Adding (1) and (2), we get

2bx = 2a

or, x = a/b

On subtraction, from (1) and (2), we get

2cy = 2b

or, y = b/c

∴ the required solution is x = a/b, y = b/c