Question

solve by elimination: ax+by-a+b=0 . bx-ay-a-b=0

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The solution of the equations is x=1 and y=-1.

Step-by-step explanation:

Given : Equations $ax+by-a+b=0$ and $bx-ay-a-b=0$

To find : Solve the equation by elimination method?

Solution :    

Let $ax+by=a-b$ ....(1)

and $bx-ay=a+b$ ....(2)

To eliminate y multiply (1) by a and (2) by b,

$a^2x+aby=a^2-ab$ ....(3)

$b^2x-aby=ab+b^2$ ......(4)

Add (3) and (4),

$a^2x+aby+b^2x-aby=a^2-ab+ab+b^2$

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

$x=\frac{a^2+b^2}{a^2+b^2}$

$x=1$

In similar way,

To eliminate x multiply (1) by b and (2) by a,

$abx+b^2y=ab-b^2$ ....(5)

$abx-a^2y=a^2+ab$ ......(6)

Subtract (5) and (6),

$abx+b^2y-abx+a^2y=ab-b^2-a^2-ab$

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

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

$y=-1$

Therefore, The solution of the equations is x=1 and y=-1.