Final answer:
To solve the simultaneous equations y = 2x and y = x^2 - 8, substitute the value of y from the first equation into the second equation and solve the resulting quadratic equation. The solutions for x are x = 1 + sqrt(9) and x = 1 - sqrt(9). Substituting these values back into the first equation gives the corresponding values of y.
Step-by-step explanation:
To solve the simultaneous equations y = 2x and y = x^2 - 8, we can substitute the value of y from the first equation into the second equation:
2x = x^2 - 8
Bringing all the terms to one side, we have x^2 - 2x - 8 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-8))) / (2(1))
Simplifying, we get x = (2 ± sqrt(4 + 32)) / 2
Therefore, the solutions for x are x = 1 + sqrt(9) and x = 1 - sqrt(9)
Substituting these values of x back into the first equation, we can find the corresponding y values: y = 2(1 + sqrt(9)) and y = 2(1 - sqrt(9))