Question

Find the solutions to the system of equations. Select all that apply. Y=x^2-1 y=2x-2

Answer 1

Answer:

Option C (1, 0)

Step-by-step explanation:

We have a system with the following equations:

$y = x ^ 2-1\\\\y = 2x-2$

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.

$2x-2 = x ^ 2 -1$

Simplify

$x ^ 2-2x + 1 = 0$

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

$x ^ 2-2x + 1= (x-1)(x-1)\\\\x ^ 2-2x + 1= (x-1)^2=0$

Finally the solutions are

$x = 1\\y =0$

Answer 2

Answer:

The correct answer option is C. (1,0).

Step-by-step explanation:

We are given the following equations and we are to find its solution:

$y=x^2-1$

$y=2x-2$

So we will check each point if its the solution.

A. (-1, 0):

$y=x^2-1$ ---> $0=(-1)^2-1$ ---> $0=0$

$y=2x-2$ ---> $0=2(-1)-2$ ---> $0\neq -4$

B. (-2, 0):

$y=x^2-1$ ---> $0=(-2)^2-1$ ---> $0\neq 3$

$y=2x-2$ ---> $0=2(-2)-2$ ---> $0\neq -6$

C. (1, 0):

$y=x^2-1$ ---> $0=(1)^2-1$ ---> $0=0$

$y=2x-2$ ---> $0=2(1)-2$ ---> $0=0$

D. (0, 1):

$y=x^2-1$ ---> $1=(0)^2-1$ ---> $1\neq -1$

$y=2x-2$ ---> $1=2(0)-2$ ---> $1\neq -2$