Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1

First Step:

I believe here it is important to firstly look at each equation on its own and just try to think how the examiner would want you to answer this type of question.

Second Step:

Recognise that both equations have an individual y in them therefore we can use this connection to solve the equation through substitution.

By Substitution we get:

x + 2x^2 + 3x - 1 + 3 = 0

which then simplies to:

2x^2 + 4x + 2  

and then divide everything by 2 gets you:

x^2 + 2x +1 = 0 

Answer:

(x+1)^2 = 0  

x = -1 (repeated root) and y = -2