Find the solution to the system

y = 2x2 - 2x - 3
y = -2x + 2
A) (-1,1) and (1, -3)
B) (0, -1) and (-0.5, 0)
C) (0.5, -3.5) and (0, -3)
D) (2, 1) and (0,0)
I saw the question asked with NoU, and I had gotten the same result as the teacher, however I do not know which one it is(a,b,c, or d)

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

2 x^2 - 5 = 0
x^2 = 2.5
x = +/- sqrt 2.5
please check for typos

yeah taht is the same thing, but I don't know what answer that is. I had gotten +/- sqrt 5/2.

so there must be a typo in the question.

It shows it as

y =2x^2 -2x-3

y =-2x+2

To find the solution to the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. Let's solve the system of equations step by step to find the answer.

Given system of equations:
1) y = 2x^2 - 2x - 3
2) y = -2x + 2

To solve this system, we can set equation 1) equal to equation 2) since they both equal y:
2x^2 - 2x - 3 = -2x + 2

Now, let's simplify the equation:
2x^2 - 2x - 3 + 2x - 2 = 0
2x^2 - 5 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula in this case:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation of 2x^2 - 5 = 0:
a = 2, b = 0, c = -5

Plugging in these values into the quadratic formula:
x = (-0 ± √(0^2 - 4 * 2 * -5)) / (2 * 2)
x = ±√(40) / 4
x = ±2√(10) / 4
x = ±√(10) / 2
x = ±(√10) / 2

Now, we can substitute these values of x back into either of the original equations to find the corresponding y-values. Let's use equation 2) y = -2x + 2:

For x = (√10) / 2:
y = -2 * (√10) / 2 + 2
y = -√10 + 2

For x = - (√10) / 2:
y = -2 * (-√10) / 2 + 2
y = √10 + 2

Therefore, the solutions to the system of equations are:
(√10 / 2, -√10 + 2) and (-√10 / 2, √10 + 2)

Now, let's compare the obtained solutions with the options given:
A) (-1,1) and (1, -3)
B) (0, -1) and (-0.5, 0)
C) (0.5, -3.5) and (0, -3)
D) (2, 1) and (0,0)

None of the obtained solutions match exactly with any of the options given.

It's possible that there may have been an error in solving the equations or in the provided options. Please double-check your work or the options given.