Determine if (1,-6) and (3,14) are solutions to the system of equations:y = 4x + 2y = x2 + 5A) Both are solutions. B) Neither is a solution. C) It cannot be determined. D) Only (3,14) is a solution.

Hello,

To solve this question we want to plug in the given solutions to the given equations, to see if it fits.

The given solutions are in the order (x, y)
For (1,-6), x = 1 and y = -6
For (3,14), x = 3 and y = 14

Let's try the 1st equation and the first solution:
y = 4x + 2
-6 = 4(1) + 2
-6 is not equal to 6, so (1,-6) is already not a solution.

Let's try the second solution and the first equation:
y = 4x + 2
14 = 4(3) + 2
14 = 14, this checks out.

However, we still have to try (3,14) with the second equation, y = 2x + 5
So, we have:
14 = 2(3) + 5
14 is not equal to 11, so (3,14) is not a solution.

So, (1,-6) and (3,14) are not solutions, so the answer is B) Neither is a solution.

Hope this helps!