Question

X + y = 5
x⁴ + y⁴ = 257
Solve simultaneously.

Answer 1

`\[ x = 2, \quad y = 3 \]`

Step-by-step explanation:

To solve the system of equations x + y = 5 and x⁴ + y⁴ = 257 simultaneously, we can use substitution or elimination. In this case, substituting y = 5 - x from the first equation into the second equation:

x⁴ + (5 - x)⁴ = 257

Solving this equation leads to x = 2 and, consequently, y = 3. Therefore, the solution to the system is x = 2, \ y = 3.

Understanding different methods for solving systems of equations is crucial in algebra, providing tools for solving real-world problems and mathematical modeling.