Find the solutions to the system of equations. Select all that apply. Y=x^2-1 y=2x-2A.(-1,0)B.(-2,0)C.(1,0)D.(0,1)

Accepted Solution

Answer:Option C (1, 0)Step-by-step explanation:We have a system with the following equations: [tex]y = x ^ 2-1\\\\y = 2x-2[/tex]The first equation is a parabola. The second equation is a straight line To solve the system, substitute the second equation in the first and solve for x. [tex]2x-2 = x ^ 2 -1[/tex]Simplify [tex]x ^ 2-2x + 1 = 0[/tex]You must search for two numbers that when you add them, obtain as a result -2 and multiplying both results in 1. These numbers are -1 and -1 Therefore [tex]x ^ 2-2x + 1= (x-1)(x-1)\\\\x ^ 2-2x + 1= (x-1)^2=0[/tex]Finally the solutions are[tex]x = 1\\y =0[/tex]