Question

x + ay = b.
ax - by = c.
solve this equation

Answer 1

Its normal application, you must try to resolve it into it's components.

Answer 2

GIVEN :

The equations are x+ay=b and ax-by=c.

TO SOLVE :

The given equations by Elimination Method

SOLUTION :

Given equations can be written as below

$x+ay=b\hfill (1)$ and

$ax-by=c\hfill (2)$

Multiply the equation (1) into a we get

$ax+a^2y=ab\hfill (3)$

Now subtracting the equations (2) from (3) we get

$ax+a^2y=ab$

$ax-by=c$

(-)_(+)___(-)___________

$a^2y+by=ab-c$

$(a^2+b)y=ab-c$

∴ $y=\frac{ab-c}{a^2+b}$

Substituting the value of y in equation (1) we get

$x+a(\frac{ab-c}{a^2+b})=b$

$x=b-a(\frac{ab-c}{a^2+b})$

$=b-\frac{a^2b-ac}{a^2+b}$

$=\frac{b(a^2+b)-(a^2b-ac)}{a^2+b}$

$=\frac{ba^2+b^2-a^2b+ac}{a^2+b}$

Adding the like terms

∴ $x=\frac{b^2+ac}{a^2+b}$

The values of x and y are  $\frac{b^2+ac}{a^2+b}$ and $\frac{ab-c}{a^2+b}$ respectively

The solution is ($\frac{b^2+ac}{a^2+b},\frac{ab-c}{a^2+b}$).