Solve: `a^2x+b^2y=c^2; b^2x+a^2y=d^2`

Solve the following system of equations by method of cross-multiplication: a^2x+b^2y=c^2,\ \ \ \ b^2x+a^2y=d^2

Solve the following system of equations by method of cross-multiplication: a^(2)x+b^(2)y=c^(2),quad b^(2)x+a^(2)y=d^(2)

Solve : a(x+y)+b(x-y)=a^2-a b+b^2 , a(x+y)-b(x-y)=a^2+a b-b^2

Solve: (a-b)x+(a+b)y=a^2-2ab-b^2 and (a+b)(x+y)=a^2+b^2

Solve: x+y=a+b ; a x-b y=a^2-b^2

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

Solve the system of the equations: a x+b y+c z=d a^2x+b^2y+c^2z=d^2 a^3x+b^3y+c^3z=d^3 Will the solution always exist and be unique?

If x=asectheta and y=btantheta , then b^2x^2-a^2y^2= (a) a b (b) a^2-b^2 (c) a^2+b^2 (d) a^2b^2

Solve: (a - b )x + (a + b)y = a^(2) - 2ab - b^(2) and (a + b) (x + y) = a^(2) + b^(2)