Solve the pair of equations for $x$ and $y$ (linear equations in two variables)

Question

Help me with the following question of linear equations where $x,y\ne0$: $$\begin{align}\frac{a^2}{x}-\frac{b^2}{y}&=0\\\frac{a^2}{x}b+\frac{b^2}{y}a&=a+b\end{align}$$

Answer 1

The 1st equation gives $\frac {a^2} {x} = \frac {b^2} {y}$ which can be plugged straight into the 2nd equation in such a way it gets rid of $x$ in that equation, you can then deduce $\frac {b^2} {y} = 1$. Solve that for $y$ and plug it back into the 1st equation and solve for $x$.

Answer 2

(Hint:) Just solve like other linear equations.You can solve two equation without the help of Matrix.

Answer 3

Take a^2/x = m and b^2/y= n Then the equations are

m-n=0,

mb+na=a+b

Solve for m and n. Then from m and n solve for x and y.