Use the elimination method to solve the linear-quadratic system y=x2+10 , y=−7x−2 .(1 point) Responses
(3,−23) and (4,−30)
(−4,26)
(−3,19)
(−3,19) and (−4,26)
To solve the system using the elimination method, we can eliminate the variable y.
We have the equations:
y = x^2 + 10 .....(1)
y = -7x - 2 .....(2)
To eliminate y, we can set the two right-hand sides equal to each other.
x^2 + 10 = -7x - 2
Bringing all terms to one side, we get:
x^2 + 7x + 12 = 0
Now we need to factorize the quadratic equation.
(x + 3)(x + 4) = 0
So the possible values for x are -3 and -4.
Substituting these values back into either equation (1) or (2), we can find the corresponding y-values.
For x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19
So one solution is (-3, 19).
For x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26
So another solution is (-4, 26).
Therefore, the correct response is (−3,19) and (−4,26).