Math, asked by myeong, 2 months ago

ax+by = a^2 - b^2 and bx + ay = 0
find x and y by elimination method
ty!

Answers

Answered by tennetiraj86
1

Step-by-step explanation:

Given :-

ax+by = a^2 - b^2 and bx + ay = 0

To find :-

find x and y by elimination method ?

Solution :-

Given pair of linear equations are

ax+by = a^2-b^2-------(1)

bx + ay = 0 --------(2)

On multiplying (1) with b then

b(ax+by) = b(a^2-b^2)

ab x + b^2 y = a^2b - b^3-----(3)

On multiplying (2) with a then

a(bx + ay) = a(0)

ab x + a^2 y = 0---------(4)

On subtracting (4) from (3)

ab x + b^2 y = a^2b - b^3

ab x + a^2 y = 0

(-)

_____________________

0+(b^2-a^2) y = a^2 b - b^3

_____________________

=> (b^2-a^2)y = a^2b-b^3

=> (b^2-a^2)y = b(a^2-b^2)

=> (b^2-a^2)y =-b(b^2-a^2)

=> y = -b(b^2-a^2)/(b^2-a^2)

=> y = - b -------(5)

On Substituting the value of y in (2)

bx + ay = 0

=> bx + a(-b) = 0

=> bx - ab = 0

=> bx = ab

=> x = ab /b

=> x = a

Therefore , x = a and y = -b

Answer:-

The solution for the given problem is

(a, -b)

Check:-

If x = a and y = -b then

ax+by = a^2 - b^2

LHS => a(a) +b(-b)

=> a^2-b^2

=> RHS

LHS = RHS is true for x= a and y = -b

and bx + ay = 0

LHS = b(a)+a(-b)

=> ba - ab

=>ab-ab

=> 0

=> RHS

LHS = RHS is true for x= a and y = -b

Verified the given relations in the given problem.

Used Method:-

  • Elimination Method
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