Question

Solve the following systems of equations
y= 3x^2 + 6x + 4

Y= -3x^2 + 4

show all work and solutions​

Answer 1

Answer:

$(-1;1)$ and $(0;4)$

Step-by-step explanation:

First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.

The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.

$3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0$

which tells us that either $x=0$ or $x=-1$

Now we can replace these value of x in one of the two to finish our work: $x=0\rightarrow y= 4$

$x=-1 \rightarrow y= -3+4=1$