Can someone please solve this for me?

Question

solve the system of equations algebraically

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

Answer 1

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

x + 1 = x^2 - 2x - 3
0 = x^2 - 3x - 4
0 = (x+1)(x-4)
x = -1, 4

y = -1+1 = 0
y = 4+1 = 5

The intersections are (-1,0) and (4,5).

Answer 2

If you have two equations and two unknowns, they you can solve for the unknowns provided the equations are related in some way. For example you just substitute x + 1 for the y in the first equation. You will get the following:

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

you now have a simple quadratic.

0 = x^2 - 3x - 4
(x+1)(x-4)

if you substitute -1 or 4 in for x on either equation you find that y can either = 0 or 5

Answer 3

take the second equation and substatute it into the first like this:

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

Now combine terms after subtracting x+1 from both sides to get:

x^2 - 3x - 4 = 0

Factor
(x-4)(x+1)=0
so
x = 4 OR x = -1 AND
y = 5 OR y = 0

Answer 4

equate y from botm sides

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

simplify it.

If you cant make factors then use quadratic roots formula to find x

once you get x , calculate y .