Final answer:
To solve the given simultaneous equations, substitute y from the second equation into the first, expand, and solve the resulting quartic equation to find 'x'. Then use 'x' to find 'y' for the final pairs of values.
Step-by-step explanation:
The question asks to algabraically solve the simultaneous equations x² * y² = 25 and y = 2x - 2.
Firstly, we can express y² as (2x - 2)² when we substitute the second equation into the first. So the first equation becomes x² * (2x - 2)² = 25. Expanding (2x - 2)² gives us 4x² - 8x + 4, and the first equation turns into x² * (4x² - 8x + 4) = 25.
Next, we can expand x² * (4x² - 8x + 4) to get 4x⁴ - 8x³ + 4x² = 25. This produces a quartic equation that we can solve for 'x'. However, without further instruction or context in how to solve this quartic equation, we may need numerical methods or algorithms for finding the roots of the equation.
Once we find the solutions for 'x', we can then substitute those values back into the second equation y = 2x - 2 to find the corresponding 'y' values. This will give us the final pairs of values (x, y).