Question

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

Answer 1

Answer:

solution is

$x=a^2$ and $y=b^2$

Step-by-step explanation:

The given equations can be written as

$bx-ay=(a-b)ab$..............(1)

$ax+by=a^3+b^3$............(2)

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

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

Adding we get

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

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

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

$x=a^2$

put $x=a^2$ in (2)

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

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

$by=b^3$

$y=b^2$

solution is

$x=a^2$ and $y=b^2$

Answer 2

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