Question

The following system of linear equations is shown in the graph.

y equals one fourth times x minus 1
x − 4y = 4

a coordinate plane with two lines that pass through the points 0 comma negative 1 and 4 comma 0

How many solutions does the system of linear equations have?

No solution
Infinitely many solutions
One solution at (4, 0)
One solution at (0, −1)

Answer 1

The system of linear equations is given as:

y = 1/4x - 1

x - 4y = 4

To find the solution, we can substitute y in the second equation with 1/4x - 1:

x - 4(1/4x - 1) = 4

x - x + 4 = 4

4 = 4

The equation 4 = 4 is always true, which means that the system of linear equations has infinitely many solutions.

Therefore, the answer is:

Infinitely many solutions.