To solve the system of equations, we need to set the two equations equal to each other because they both equal y.

So, we have:

x^2 + 11 = 2x^2 + 2

Next, we rearrange the equation to isolate terms with x:

2x^2 - x^2 = 11 - 2

This simplifies to:

x^2 = 9

Taking the square root of both sides gives us the solutions for x:

x = 3 and x = -3

We then substitute x = 3 and x = -3 into the first equation y = x^2 + 11 to find the corresponding y values:

For x = 3, y = (3)^2 + 11 = 9 + 11 = 20
For x = -3, y = (-3)^2 + 11 = 9 + 11 = 20

So, the solutions to the system of equations are (3, 20) and (-3, 20), which corresponds to option d.

Question

To solve the system of equations, we need to set the two equations equal to each other because they both equal y.

So, we have:

x^2 + 11 = 2x^2 + 2

Next, we rearrange the equation to isolate terms with x:

2x^2 - x^2 = 11 - 2

This simplifies to:

x^2 = 9

Taking the square root of both sides gives us the solutions for x:

x = 3 and x = -3

We then substitute x = 3 and x = -3 into the first equation y = x^2 + 11 to find the corresponding y values:

For x = 3, y = (3)^2 + 11 = 9 + 11 = 20
For x = -3, y = (-3)^2 + 11 = 9 + 11 = 20

So, the solutions to the system of equations are (3, 20) and (-3, 20), which corresponds to option d.

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