The two solutions of the system are (-2.58, -68.64) and (18.58, 100.32).
How to solve the system of equations?
Here we have the two equations:
[tex]y = 24x - x^2[/tex]
[tex]y = 8x - 48[/tex]
To solve it, we notice that y is isolated in the two equations, then we can write:
[tex]8x - 48 = 24x - x^2[/tex]
Now we can just solve that quadratic equation.
[tex]24x - x^2 - 8x + 48 = 0\\\\-x^2 + 16x + 48 = 0[/tex]
If we use Bhaskara's formula, we get:
[tex]x = \frac{-16 \pm \sqrt{(16)^2 - 4*(-1)*48} }{-2} \\\\x = \frac{-16 \pm \sqrt{448} }{-2}\\\\x = 8 \pm \sqrt{112}[/tex]
Then the two solutions are:
x = 8 + 10.58 = 18.58
x = 8 - 10.58 = -2.58
To get the complete solutions, we need to evaluate one of the equations in these two x-values, let's evaluate the linear one.
y = 8*(-2.58) - 48 = -68.64
y = 8*(18.58) - 48 = 100.32
So the two solutions are (-2.58, -68.64) and (18.58, 100.32).
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
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