Use the elimination method to solve the linear-quadratic system y = x^2 + 10, y= -7x -2.
• (3, -23) and (4,-30)
• (-3,19) and (-4,26)
• (-3,19)
• (-4,26)
First, let's substitute the equation y = x^2 + 10 into the second equation:
x^2 + 10 = -7x - 2
Now, let's rearrange this equation into standard quadratic form:
x^2 + 7x + 12 = 0
This equation can be factored as:
(x + 3)(x + 4) = 0
So, x + 3 = 0 or x + 4 = 0
x = -3 or x = -4
Now that we have the x-values, we can substitute them back into either equation to find the corresponding y-values.
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 solution to the system of equations y = x^2 + 10 and y = -7x - 2 is the ordered pairs (-3, 19) and (-4, 26).