x/a-y/b=2 and ax-by=a²-b²
Question from Linear Equation In Two Variables
Answers
★QUESTION
- x/a-y/b=2 and ax-by=a²-b²
★ANSWER
- x=a and y=b
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★SOLUTION
X/a+y/b=2
Bx+ay/ab=2 (Lcm)
Bx+ay=2ab (*a)______(I)
Ax-by=a^2-b^2 (*b)_____(II)
Eliminating eq(ii) from eq(i)
Abx+a²y=2a²b
Abx-b²y=a²b-b³
- + -
------------------------------------
A^2y+b^2y=2a^2b-(a^2b-b^3)
y(a^2+b^2)= 2a^b-a^2b+b^3
y(a^2+b^2)= a^2b+b^3
y(a^2+b^2)= b(a^2+b^2)
y = b_____(III)
Putting eq(iii) in eq(i)
bx+ay=2ab
bx+a(b)=2ab
→ bx=2ab-ab
→ bx=ab
→ x=ab/b
→ x=a
So, x=a and y=b
Step-by-step explanation:
X/a+y/b=2
Bx+ay/ab=2 (Lcm)
Bx+ay=2ab (*a)______(I)
Ax-by=a^2-b^2 (*b)_____(II)
Eliminating eq(ii) from eq(i)
Abx+a²y=2a²b
Abx-b²y=a²b-b³
- + -
------------------------------------
A^2y+b^2y=2a^2b-(a^2b-b^3)
y(a^2+b^2)= 2a^b-a^2b+b^3
y(a^2+b^2)= a^2b+b^3
y(a^2+b^2)= b(a^2+b^2)
y = b_____(III)
Putting eq(iii) in eq(i)
bx+ay=2ab
bx+a(b)=2ab
→ bx=2ab-ab
→ bx=ab
→ x=ab/b
→ x=a
So, x=a and y=b