To solve this system of equations, we can substitute the second equation into the first equation:

x² + (1/2)x² - 5 = 100

Combining like terms:

(3/2)x² - 5 = 100

Add 5 to both sides:

(3/2)x² = 105

Divide by 3/2 on both sides:

x² = 105 * 2 / 3
x² = 70

Taking the square root of both sides:

x = ±√70

Now, substitute the value of x back into the second equation to solve for y:

y = (1/2)(√70)² - 10
y = (1/2)(70) - 10
y = 35 - 10
y = 25

Therefore, the solutions to the system of equations are x = ±√70 and y = 25.