Question

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.

Answer 1

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.