x/a-y/b=a-b ax+by=a3+b3 slove by elimination method

Answer:

solution is

[tex]x=a^2[/tex] and [tex]y=b^2[/tex]

Step-by-step explanation:

The given equations can be written as

[tex]bx-ay=(a-b)ab[/tex]..............(1)

[tex]ax+by=a^3+b^3[/tex]............(2)

[tex](1)*b\implies\:b^2x-aby=(a-b)ab^2[/tex]

[tex](2)*a\implies\:a^2x+aby=a(a^3+b^3)[/tex]

Adding we get

[tex](a^2+b^2)x=a^2b^2-ab^3+a^4+ab^3[/tex]

[tex](a^2+b^2)x=a^2b^2+a^4[/tex]

[tex](a^2+b^2)x=a^2(a^2+b^2)[/tex]

[tex]x=a^2[/tex]

put [tex]x=a^2[/tex] in (2)

[tex]a(a^2)+by=a^3+b^3[/tex]

[tex]a^3+by=a^3+b^3[/tex]

[tex]by=b^3[/tex]

[tex]y=b^2[/tex]

solution is

[tex]x=a^2[/tex] and [tex]y=b^2[/tex]

Step-by-step explanation:

The given equations can be written as

bx-ay=(a-b)abbx−ay=(a−b)ab ..............(1)

ax+by=a^3+b^3ax+by=a

3

+b

3

............(2)

(1)*b\implies\:b^2x-aby=(a-b)ab^2(1)∗b⟹b

2

x−aby=(a−b)ab

2

(2)*a\implies\:a^2x+aby=a(a^3+b^3)(2)∗a⟹a

2

x+aby=a(a

3

+b

3

)

Adding we get

(a^2+b^2)x=a^2b^2-ab^3+a^4+ab^3(a

2

+b

2

)x=a

2

b

2

−ab

3

+a

4

+ab

3

(a^2+b^2)x=a^2b^2+a^4(a

2

+b

2

)x=a

2

b

2

+a

4

(a^2+b^2)x=a^2(a^2+b^2)(a

2

+b

2

)x=a

2

(a

2

+b

2

)

x=a^2x=a

2

put x=a^2x=a

2

in (2)

a(a^2)+by=a^3+b^3a(a

2

)+by=a

3

+b

3

a^3+by=a^3+b^3a

3

+by=a

3

+b

3

by=b^3by=b

3

y=b^2y=b

2

solution is

x=a^2x=a

2

and y=b^2y=b

2