Question

ax+by=a-b, bx-ay=a+b,. Solve the pair of leniar equations​

Answer 1

Answer:

hi

Step-by-step explanation:

ax+by=a-b

ax=a-b-by

x=a-b-by/a←

bx-ay=a+b

substituting

b(a-b-by/a)-ay=a+b

ab-b²-b²y/a-ay=a+b

ab-b²-b²y-a²y/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

(b²+a²)y=-(a²+b²)

y=-(a²+b²)/a²+b²

y=-1←

substituting value of y

x=a-b-b(-1)/a

x=a-b+b/a

x=a/a

x=1

Answer 2

Answer:

ax + by = a - b.................(1)

bx - ay = a + b.....................(2)

Taking (1),

ax + by = (a - b)

⇒ x = (a - b - by)/a

Substituting the value of x in (2), we get,

b{(a - b - by)/a} - ay = a + b

⇒ ab - b² - b²y - a²y = a² + ab

⇒ -y (a² + b²) = a² + b² + ab - ab

⇒ -y (a² + b²) = (a² + b²)

⇒ -y = 1

⇒ y = -1

Substituting y = -1 in (1), we get,

ax + b(-1) = a - b

⇒ ax - b = a - b

⇒ ax = a

⇒ x = 1

Hope it helps you...