Final answer:
To solve the simultaneous equations x²y² = 25 and y = 2x - 2, perform a substitution of the y value from the second equation into the first, then solve the resulting polynomial for x and use these solutions to find the corresponding y values.
Step-by-step explanation:
To solve the simultaneous equations x²y² = 25 and y = 2x - 2 algebraically, we can use substitution since one equation is already solved for y. Substituting y from the second equation into the first equation, we get:
x²(2x - 2)² = 25
Expand and simplify the equation to find the possible values of x:
x²(4x² - 8x + 4) = 25
4x⁴ - 8x³ + 4x² - 25 = 0
This can then be solved by factoring or using the quadratic formula if it simplifies to a quadratic equation; otherwise, numerical methods can be used for higher-degree polynomials. After finding the values of x, plug them back into the equation y = 2x - 2 to find the corresponding values of y. There might be multiple solutions for the variables x and y.
Note: The other information provided with the question regarding dx²-y², 2Py, or other unrelated values and equations does not apply to the solution for the given simultaneous equations and should be ignored in this context.