Question

solve for x and y :ax+by=a-b; bx-ay=a+b

pls write steps

Answer 1

Ax+by=a-b

ax=a-b-by

x=a-b-by/a←

bx-ay=a+b

substituting

b(a-b-by/a)-ay=a+b

ab-b²-b²y/a-ay=a+b

ab-b²-b²y-a²y/a=a+b

ab-b²-(b²+a²)y=a²+ab

-(b²+a²)y=a²+ab-ab+b²

(b²+a²)y=-(a²+b²)

y=-(a²+b²)/a²+b²

y=-1←

substituting value of y

x=a-b-b(-1)/a

x=a-b+b/a

x=a/a

x=1

Answer 2

Answer:

The value of x is $x = \frac{-a^2+2ab+b^2}{(b^2+a^2)}$ and value of y is $y = \frac{a^2+2ab-b^2}{(b^2+a^2)}$

Step-by-step explanation:

We can solve this equation by simultaneous linear equation method

It is given to us that
$ax+by=a-b\\bx-ay=a+b$

Now by using coefficient multiplication we get
$abx+b^2y=ab-b^2\\abx-a^2y=a^2+ab$

After subtracting the equation from one another we get
$(b^2+a^2)y = a^2+2ab-b^2\\y = \frac{a^2+2ab-b^2}{(b^2+a^2)}$

And the value of x is
$(b^2+a^2)x = -a^2+2ab+b^2\\x = \frac{-a^2+2ab+b^2}{(b^2+a^2)}$

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