How to solve to system y=x^2-2 y=2x+1

the solutions are (3, 7) and (-1, - 1)

Step-by-step explanation:

Insert the " = " symbol between the two equations, obtaining:

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

Then x^2 - 2 = 2x + 1, or

x^2 - 2x - 3 = 0, and this can be factored into (x - 3) (x + 1) = 0.

Thus, the x values that satisfy this system are {-1, 3}.

Use y = 2x + 1 to find the corresponding y values:

y = 2 (-1) + 1 = - 1

and

y = 2 (3) + 1 = 7

Then the solutions are (3, 7) and (-1, - 1)