Final answer:
The system of equations 2x-y=-5 and 8x-4y=20 has no solution.
Step-by-step explanation:
To determine whether the system of equations 2x-y=-5 and 8x-4y=20 has one and only one solution, we can use the method of substitution or elimination.
Let's use the method of elimination:
Multiply the first equation by 4 to make the y-coefficients equal: 8x-4y=-20.
Now, subtract the second equation from the modified first equation: (8x-4y)-(8x-4y)=-20-20.
When the lines are parallel, there is no point of intersection, and the system has no solution. Therefore, the system of equations 2x-y=-5 and 8x-4y=20 has no solution, and it does not have one and only one solution.
Simplifying, we have 0=-40. This is a contradiction because 0 cannot equal -40. Therefore, the system of equations has no solution.