Question

ax+by=a-b,bx+ay=a+b by cross multiplication method.

Answer 1

Answer:

x=2ab

y=a-2a^2

Step-by-step explanation:

ax+by=a-b

bx+ay=a+b

a1=a  b1=b  c1=a-b

a2=b  b2=a  c2=a+b

x/ab+b^2-a^2+ab  =   y/a^2+ab-ab+b^2  =  1/a^2-b^2

x/2ab+b^2-a^2  =  y/a^2+b^2  =  1/a^2-b^2

x/2ab+b^2-a^2=1/a^2-b^2

(a^2-b^2)x  =  2ab+b^2-a^2

(a+b)(b-a)x = 2ab+(a+b)(b-a)

x=2ab

substitute x in eq.1

2a^b+by=a-b

y=a-b-2a^b/b

y=b(a-2a^2)/b

y=a-2a^2

Answer 2

Answer:

ax + by = a-b becomes

(ax + by)/(a - b) = 1

bx - ay = a + b becomes

(bx-ay)/(a+b) = 1

So now we can equate the two:

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

So by cross multiplication:

(ax + by)(a + b) = (bx - ay)(a - b)

a^2x + abx + aby + b^2y = abx - b^2x - a^2y + aby

a^2x + b^2y = -b^2x - a^2y

a^2x + b^2x = -a^2y - b^2y

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

x = -y

Substituting into the first equation:

-ay + by = a-b

-(a - b)y = a-b

y = -1

So x = 1