use the elimination method to solve the linear-quadratic system y=x^2 + 10, Y= -7x - 2
A: (-4, 26)
B: (-3,19)
C: (3,-23) and (4, -30)
D: (3,19) and (-4,26)
To solve this system using the elimination method, we need to set the two equations equal to each other and solve for x.
x^2 + 10 = -7x - 2
x^2 + 7x + 12 = 0
(x+3)(x+4) = 0
x = -3 or x = -4
Now that we have the values of x, we can substitute them back into either equation to find the corresponding values of y.
When x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19
When x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26
Therefore, the solution to the system is (-3, 19) and (-4, 26), which corresponds to option D.