To solve the system using the elimination method, we need to eliminate one variable by manipulating one or both of the equations.
Equation 1: y = x^2 + 10
Equation 2: y = -7x - 2
Since both equations are already solved for y, we can set them equal to each other:
x^2 + 10 = -7x - 2
Next, we rearrange the equation to bring all terms to one side and set it equal to zero:
x^2 + 7x + 12 = 0
Now we can factor this quadratic equation:
(x + 3)(x + 4) = 0
Setting each factor equal to zero:
x + 3 = 0 -> x = -3
x + 4 = 0 -> x = -4
So the possible x-values are x = -3 and x = -4.
Now, we substitute these x-values back into either Equation 1 or Equation 2 to find the corresponding y-values.
Using Equation 1: y = (-3)^2 + 10 -> y = 9 + 10 -> y = 19
Using Equation 1: y = (-4)^2 + 10 -> y = 16 + 10 -> y = 26
Therefore, the solution to the system is (-3, 19) and (-4, 26).