The system has solutions (6, 312) and (-6, 312) and the correct option is C.
Here's how we can solve the system of equations and find the solutions:
1. Solve for y in the second equation:
Divide both sides of the equation 2y = 16x^2 + 48 by 2:
y = 8x^2 + 24
2. Substitute this expression for y in the first equation:
Replace y in 10x^2 - y = 48 with the expression we obtained:
10x^2 - (8x^2 + 24) = 48
Combine like terms:
2x^2 - 24 = 48
Add 24 to both sides:
2x^2 = 72
3. Solve for x:
Divide both sides by 2:
x^2 = 36
Take the square root of both sides:
x = +/-6
4. Substitute the values of x back into the equation y = 8x^2 + 24:
For x = 6:
y = 8(6)^2 + 24 = 312
For x = -6:
y = 8(-6)^2 + 24 = 312
Therefore, the solutions of the system are:
(x, y) = (6, 312) and (-6, 312)
This eliminates options A, B, and D, leaving only option C as the correct answer.
Question:
What are the solutions of the following system? { 10x^2-y=48 and 2y=16x^2+48
A) (2 sqrt3, 120) and (-2 sqrt3, 120)
B) (2 sqrt3, 120) and (-2 sqrt 3, -72)
C) (6, 312) and (-6, 312)
D) (6, 312) and (-6,-264)