Question

Question #5eee2

Answer 1

I will assume that you are treating `a` and `b` as constants, and are trying to solve for `x` and `y`.

We will solve the first equation for `x`:

`x = yab`

Now, substitution into the second equation gives:

`a^2 by + by = a^2 + b^2`

Factor out `y`:

`y(a^2 b + b) = a^2 + b^2`

And lastly, divide:

`y = (a^2 + b^2)/(a^2 b + b)`

So there's `y`. To solve for `x`, we will revisit the first equation, this time solving for `y`:

`y = x/(ab)`

Substitute into the second equation:

`ax + x/a = a^2 + b^2`

Factor `x`:

`x(a + 1/a) = a^2 + b^2`

And lastly, divide to isolate `x`:

`x = (a^2 + b^2)/(a + 1/a)`

If we would like, we can rewrite `a + 1/a` as `(a^2 + 1)/a`:

`x = (a^2 + b^2)/((a^2 + 1)/a)`

And then simplify a bit, just to make the equation a little prettier:

`x = (a^3 + b^2 a)/(a^2 + 1)`