Q. 31

# Solve for x and y:ax + by-a + b = 0, bx-ay-a-b = O.

Eqn1 : ax + by - a + b = 0

ax + by = a - b

Multiplying both side by b

abx + b2y = ab - b2 …[1]

Eqn2 : bx - ay - a - b = 0

bx - ay = a + b

Multiplying both side by a

abx - a2y = a2 + ab …[2]

Subtracting [2] from [1]

abx - a2y - (abx + b2y) = a2 + ab - (ab - b2)

abx - a2y - abx - b2y = a2 + ab - ab + b2

-y(a2 + b2) = a2 + b2

-y = 1

y = 1

Putting value of y in eqn1, we get

ax + b(-1) - a + b = 0

ax - b - a + b = 0

ax = a

x = 1

So, x = 1 and y = -1

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