By solving the system of equations, we can see that the solutions are:
(A, B) = (4, 9)
(C, D) = (1, -6).
<h3>How to solve the system of equations?</h3>
Here we have the following system of equations:
x^2 - y = 7
y - 5x = -11
If we isolate the variable y in both equations, we get:
y = x^2 - 7
y = -11 + 5x
Now we can equate these two to get:
x^2 - 7 = -11 + 5x
now we have a quadratic equation, this can be rewritten as:
x^2 - 7 + 11 - 5x = 0
x^2 - 5x + 4 = 0
Using the quadratic formula, we will see that the solutions are:
![x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B%28-5%29%5E2%20-%204%2A1%2A%284%29%7D%20%7D%7B2%2A1%7D)
Solving that we get:
![x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B%289%7D%20%7D%7B2%7D%20%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B5%20%5Cpm%203%7D%7B2%7D)
So the two solutions for x are:
x = (5 + 3)/2 = 4
x = (5 - 3)/2 = 1
Evaluating the second equation in these x-values we get:
y = -11 + 5*4 = -11 + 20 = 9
y = -11 + 5*1 = -6
Then we have the coordinate pairs: (4, 9) (on the first quadrant) and (1, -6) on the fourth quadrant.
Learn more about systems of equations:
brainly.com/question/13729904
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