The algebraic solutions to the system of equations are given as follows:
[tex](3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)[/tex]
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the equations are:
Replacing the second equation in the first:
x² + (2x - 2)² = 25
x² + 4x² - 8x + 4 = 25
5x² - 8x - 21 = 0.
Which is a quadratic equation with coefficients a = 5, b = -8, c = -21, then:
[tex]\Delta = (-8)^2 - 4(5)(-21) = 484[/tex]
[tex]x_1 = \frac{-(-8) + \sqrt{484}}{2(5)} = 3[/tex]
[tex]x_2 = \frac{-(-8) - \sqrt{484}}{2(5)} = -\frac{7}{5}[/tex]
Then, the solutions for y are:
Thus, the solutions are:
[tex](3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
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