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