Solving systems of linear and quadratic equations using elimination...I can;t figure out how to do these problems,can someone explain please?

Question

anonymous · Answer

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

anonymous · Answer

$$
-x+3=x^2+1 \implies x^2+x-2=0
$$

anonymous · Answer

OK but how do I get to that answer?That's what I don't understand.

anonymous · Answer

Equality is transivitve: $$
y=-x+3\
y=x^2+1\
-x+3 = y=x^2+
$$

anonymous · Answer

There are two ways you could do this.
Subtract equation 1 from equation 2. (Elimination)

Solve for one variable and replace it into the other equation (Substitution)

anonymous · Answer

Ok,that makes sense,thank you :)

anonymous · Answer

Ok so if I have the systems,y=x^2 and y+x+2...would they equal x^2-x+2?

anonymous · Answer

Using substitution on the equations, you get: $$
-x+3=x^2+1
$$Then you subtract $-x+3$ form both sides:$$
0 = x^2+1-(-x+3) = x^2+1+x-3=x^2+x-2
$$Or simply put: $$
0 = x^2+x-2
$$This can be solved with the quadratic formula.

anonymous · Answer

You don't need the quadratic formula. This can be factored normally.$$x^2+x-2=0 \rightarrow (x+2)(x-1)=0 \rightarrow x=-2,1$$
@DogLuverSarah2012