Question

Solve the x and y ,ax+by = b-a , bx-ay = -(a+b)

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Answer 1

Solution

Given :-

• ax + by = b - a ------------(1)
• bx - ay = -(a+b)-----------(2)

Find :-

• Value of x & y

Explanation

By , Elimination Method

Multiply by b in equ(1) & a in equ(2)

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

______________Sub. it's (Eliminate x)

➩ b²y + a²y = (b²-ab)+(a²+ab)

➩ y (a² + b²) = a² + b² - ab + ab

➩ y (a² + b²) = a² + b²

➩ y = (a² + b²)/(a² + b²)

➩ y = 1

Keep Value of y in equ(1)

➩ ax + b*1 = b - a

➩ ax = b - a - b

➩ ax = -a

➩ x = -a/a

➩ x = -1

_________________

Hence

• Value of x will be = -1
• Value of y will be = 1

________________

Verification of Answer

Case(1).

Keep value of x & y in equ(1)

➩ a * (-1) + b*1 = b - a

➩ -a + b = b - a

Or

➩ (b - a) = (b - a)

L.H.S. = R.H.S.

_________________________

Case(2).

Again, Keep value of x & y in equ(2)

➩ b * (-1) - a * 1 = -(a + b)

➩ -b - a = -(a+b)

➩ -(a+b) = -(a+b)

L.H.S. = R.H.S.

________________________

Here, Case(1) & Case(2) are proved .

Since, we can say that our solution will be correct .

_________________

Answer 2

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