I'll use the substitution method to demonstrate that there aren't specific values for x and y that solve the system:
1. Solve one equation for one variable:
Choose the first equation, 2x + 4y = 10, and solve for x:
2x = 10 - 4y
x = 5 - 2y
2. Substitute into the second equation:
Substitute the expression for x into the second equation, 4x + 8y = 20:
4(5 - 2y) + 8y = 20
3. Simplify and solve:
20 - 8y + 8y = 20
20 = 20
4. Observe the result:
The equation 20 = 20 is always true, regardless of the values of x and y. This means there are infinitely many solutions that satisfy both equations.
Conclusion:
We cannot find a unique solution for x and y in this system because the equations represent the same line. Any point on that line will make both equations true.
