Tell whether the system has one solution, infinitely many solutions, or no solution. −x+4y=−1 5x−20y=5 (1 point) Responses The system has one solution. The system has one solution. The system has no solution. The system has no solution. The system has infinitely many solutions.
To determine whether the system has one solution, infinitely many solutions, or no solution, we can use the method of substitution.
We can start by solving the first equation for x:
-x + 4y = -1
=> x = 4y - 1
Now, substitute this value of x into the second equation:
5(4y - 1) - 20y = 5
20y - 5 - 20y = 5
-5 = 5
As the equation -5 = 5 is false, there is no value of y that satisfies the system of equations. Therefore, the system has no solution.