Question

plz solve it with substitution method ax+by-a+b=0 bx-ay-a-b=0​

Answer 1

Question

plz solve it with substitution method ax+by-a+b=0 , bx-ay-a-b=0

Solution

Given:-

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

Find:-

• Value of x and y

Explanation

Substitution method .

By, equ(1)

➠ x = [(a-b)-by]/a -------------(3)

Substitute value of x in equ(2),

➠ b.[(a-b)-by]/a - ay = (a+b)

➠ b.(a-b)/a-b²y/a - ay = (a+b)

➠ (ab-b²)/a - (a+b) = b²y/a + ay

➠(ab-b²-a²-ab)/a = (b²+a²)y/a

➠ y = -(a²+b²)/a²+b²)

➠ y = -1

keep value of y in equ(1)

➠ax + b.(-1) = a-b

➠ ax = a-b+b

➠ax = a

➠x = a/a

➠x = 1

Thus

• value of x = 1
• Value of y = -1

___________________

Verification

Keep value of x and y in equ(1)

➠a.1 + b.(-1) = a-b

➠ a - b = a - b

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

That's proved.

___________________

Answer 2

Answer:

Question

plz solve it with substitution method ax+by-a+b=0 , bx-ay-a-b=0

Solution

Given:-

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

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

Find:-

Value of x and y

Explanation

Substitution method .

By, equ(1)

➠ x = [(a-b)-by]/a -------------(3)

Substitute value of x in equ(2),

➠ b.[(a-b)-by]/a - ay = (a+b)

➠ b.(a-b)/a-b²y/a - ay = (a+b)

➠ (ab-b²)/a - (a+b) = b²y/a + ay

➠(ab-b²-a²-ab)/a = (b²+a²)y/a

➠ y = -(a²+b²)/a²+b²)

➠ y = -1

keep value of y in equ(1)

➠ax + b.(-1) = a-b

➠ ax = a-b+b

➠ax = a

➠x = a/a

➠x = 1

Thus

value of x = 1

Value of y = -1

________________________

Verification

Keep value of x and y in equ(1)

➠a.1 + b.(-1) = a-b

➠ a - b = a - b

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

That's proved.

________________________