Solving system of equations

Question

I've been learning about solving systems of equations by substitution or elimination or whatever but I have trouble figuring out which one is easiest to use and when. I think I am doing this all wrong though. I can solve them anyway but it still isn't working and I keep getting stuck.

So one system is x²+y²=16 

                             x²-4y²=16. I hate square roots in the first place anyways.

So I was doing substitution and I solved the first equation by y²=plus or minus the square root of -x²+16 and the second equation and x=plus or minus the square root of 4y²+16 and I don't know how to substitute what next.

 

My other system is x+y=-2

                               y=x²-5x. I figured this would be easier because it didn't look like as tough of a problem as the other one. So I plugged in the second equation into the first equation as y. So x+(x²-5x)=-2 and solved to get x²-4x+2=0. I tried to factor this but it's where I got stuck and stopped. I can't seem to figure these out and I need help please!! :/ 

Answer 1

the first 2 equations... lets subtract them from each other before substitution.

I think you should get y=0

You can solve the rest.

 

In the second one, if you cannot factor it, it means the answers are not whole numbers. This means you have to use the quadratic formula. Do you remember how to use it?
negative B plus or minus the root of B squared minus 4 A C all over 2 A [it looks better if you have the actual equation]

 

And again, try putting your two equations into this graphing calculator and see what it gives you.

https://www.desmos.com/calculator