Solve using cross multiplication method, ax + by = a^2 ; bx + ay = b^2

x=a²+ab+b²/a+b , y=-ab/a+b

Step-by-step explanation:

The system of the given equation may b written as:

ax+by-a²=0

bx+ay-b²=0

Here,

a1=a,b1=b,c1= -a²

a2=b,b2=a and c2= -b²

By cross multiplication we get

x/b*(-b²)-(-a²)*a = -y/a*(-b²)-(-a²)*b = 1/a*a-b*b

x/-b³+a³ = -y/-ab²+a²b  = 1/a²-b²

Now

x/-b³+a³ = 1/a²-b²

x=a³-b³/a²-b²

x=(a-b)(a²+ab+b²)/(a-b)(a+b)

x=a²+ab+b²/a+b

And,

-y/-ab²+a²b = 1/a²-b²

-y=a²b -ab²/a²-b²

y=ab²-a²b/a²-b²

y=ab(b-a)/(a-b)(a+b)

y= -ab(a-b)/(a-b)(a+b)

y= -ab/a+b

Hence x=a²+ab+b²/a+b , y=-ab/a+b