## Solve by Cramer’s method : ax +by = a – b ; bx = ay + a + b ,where ‘a; and ‘b’ are constants and both are not zero.

Question

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## Answers ( )

The given equations are

ax + by = a – b …..(i)

bx – ay = a + b …..(ii)

We solve the problem by Cramer’s method

Thus we multiply (i) by b and (ii) by a. We get

abx + b²y = ab – b²

abx – a²y = a² + ab

On subtraction, we get

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

⇒ (a² + b²) y = – (a² + b²)

⇒ y = – 1

Putting y = – 1 in (i), we get

ax + (- 1) b = a – b

⇒ ax – b = a – b

⇒ ax = a

⇒ x = 1, where a ≠ 0

∴ the required solution be

x = 1 and y = – 1

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Answer:The given equations are

ax + by = a – b …..(i)

bx – ay = a + b …..(ii)

We solve the problem by Elimination Method.

Thus we multiply (i) by b and (ii) by a. We get

abx + b²y = ab – b²

abx – a²y = a² + ab

On subtraction, we get

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

⇒ (a² + b²) y = – (a² + b²)

⇒ y = – 1

Putting y = – 1 in (i), we get

ax + (- 1) b = a – b

⇒ ax – b = a – b

⇒ ax = a

⇒ x = 1, where a ≠ 0

∴ the required solution be

x = 1 and y = – 1