Solve by Cramer's method : ax +by = a - b ; bx = ay + a + b ,where 'a; and 'b' are constants and both are not zero.
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
hope this helps you.
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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