Use the substitution method to find the solutions to the linear-quadratic system y=x2−x−40 , y=−3x−5 ?(1 point)
1. (5,6-10)
2. (-7,26)
3. (5,-20) and (-7,16)
4. (5,-10) and (-7,26)
To use the substitution method, we set the two equations equal to each other:
x^2 - x - 40 = -3x - 5
Now, rearrange to get the equation in standard form:
x^2 + 2x - 35 = 0
Factor the quadratic equation:
(x + 7)(x - 5) = 0
This gives us two possible values for x: x = -7 and x = 5
Now substitute these values back into one of the original equations to find the corresponding y values:
For x = -7:
y = -3(-7) - 5
y = 21 - 5
y = 16
For x = 5:
y = 5^2 - 5 - 40
y = 25 - 5 - 40
y = -20
Therefore, the solutions to the system are (5, -20) and (-7, 16).
So, the correct answer is 3. (5,-20) and (-7,16).