Are there any tricks for simultaneous equations I should be aware of?

Question

I'm at the end of a difficult logarithms question and have ascertained the linear equations I need in order to establish x and y as the questions asks of me.

The equations are:

$x - 5y + 4 = 1$

$\frac {x+1}{2} = y^2$

Now I'm going through slowly, doing to each side the same thing, so as not to ruin my equations. I've got to....

$x + 3 = 5y$

$x + 1 = 2y^2$

I just wondered if there is a trick somewhere that would speed things up for me?

Thank you

Answer 1

You can see $5y-2y^2=2$ by subtracting the 2 equations. Then solve the quadratic.