Question

Solve for x and y:
$\frac{x}{a} - \frac{y}{b} = a - b$
and
$ax + by = {a}^{3} + {b}^{3}$

Answer 1

HI,
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1)   SOLVE FOR  X FIRST:-

Step 1: Multiply both sides by ab.

−ay+bx=$a^{2}$b−a$b^{2}$

Step 2: Add ay to both sides.


−ay+bx+ay=$a^{2}$b−a$b^{2}$+ay

bx=$a^{2}$b−a$b^{2}$+ay


Step 3: Divide both sides by b.


$\frac{bx}{b}= \frac{a^2b-ab^2+ay}{b}$


$x=\frac{a^2b-ab^2+ay}{b}$   
  Answer
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LET'S SOLVE FOR "Y"

1)    Step 1: Multiply both sides by ab.

−ay+bx=$a^{2}$b−a$b^{2}$


Step 2: Add -bx to both sides.


−ay+bx+−bx=$a^{2}$b−a$b^{2}$+−bx


−ay=$a^{2}$b−a$b^{2}$−bx

Step 3: Divide both sides by -a.

$\frac{-ay}{-a} = \frac{a^2b-ab^2-bx}{-a}$

y = $\frac{-a^2b+ab^2+bx}{a}$

 Answer
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NOW THE 2ND QUESTION
LETS SOLVE FOR "X"

1)  Step 1: Add -by to both sides.

ax+by+−by=a3+b3+−by

ax=a3+b3−by

Step 2: Divide both sides by a.


$\frac{ax}{a}$=$\frac{a^3+b^3-by}{a}$


x=$\frac{a^3+b^3-by}{a}$ Answer
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LETS SOLVE FOR "Y"

Step 1: Add -ax to both sides.

ax+by+−ax=$a^{3}$+$b^{3}$+−ax

by=$a^{3}$+$b^{3}$−ax

Step 2: Divide both sides by b.

$\frac{by}{b} = \frac{a^3+b^3-ax}{b}$


y = $\frac{a^3+b^3-ax}{b}$
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HOPE THIS HELPS YOU :)