Question

Use the elimination method to solve the linear-quadratic system y=x2+10, y=−7x−2.(1 point)
Responses

(−4,26)
left parenthesis negative 4 comma 26 right parenthesis

(−3,19)
left parenthesis negative 3 comma 19 right parenthesis

(−3,19) and (−4,26)
left parenthesis negative 3 comma 19 right parenthesis and left parenthesis negative 4 comma 26 right parenthesis

(3,−23) and (4,−30)

Answer 1

To solve the system using the elimination method, we need to eliminate one variable by manipulating the equations.

First, let's write the equations in standard form:
y = x^2 + 10
y = -7x - 2

To eliminate the y variable, we can set the two equations equal to each other:
x^2 + 10 = -7x - 2

Next, rearrange the equation into standard quadratic form:
x^2 + 7x + 12 = 0

Now, factor the quadratic equation:
(x + 3)(x + 4) = 0

Set each factor equal to zero and solve for x:
x + 3 = 0 or x + 4 = 0
x = -3 or x = -4

Plug these x-values back into one of the original equations to solve for y:
For x = -3:
y = (-3)^2 + 10
y = 9 + 10
y = 19

For x = -4:
y = (-4)^2 + 10
y = 16 + 10
y = 26

The solutions are (-3, 19) and (-4, 26).