To solve the system using the elimination method, we need to eliminate one variable. Since the y term in the second equation is already isolated, we can substitute it into the first equation:
x^2 + 10 = -7x - 2
Now, we have a quadratic equation. To solve it, we can move all terms to one side:
x^2 + 7x + 12 = 0
This equation can be factored as:
(x + 3)(x + 4) = 0
Setting each factor equal to zero, we get:
x + 3 = 0 or x + 4 = 0
Solving these equations, we find:
x = -3 or x = -4
Now, we substitute these values back into either of the original equations 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
Therefore, the solutions to the system are (-3, 19) and (-4, 26).
Use the elimination method to solve the linear-quadratic system y=x^2+10, y=−7x−2.
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