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).
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)
1 answer
1 answer