how many solutions does the system of equations have?

Question

x-4y=12
5x-20y=60

Answer 1

To find the number of solutions for this system of equations, we can solve the equations simultaneously.

We can begin by eliminating the x variable.

To do this, we can multiply the first equation by 5 to make the coefficients of x in both equations match:

5(x - 4y) = 5(12)
5x - 20y = 60

Now we have:

5x - 20y = 60
5x - 20y = 60

Since we have two identical equations, this implies that the two equations represent the same line.

In other words, the system of equations is dependent and has infinitely many solutions.

Geometrically, this means that the two equations represent the same line and are overlapping, so they intersect at every point on the line.