Question

How many solutions does the system have?

\[\begin{cases}
20x-5y=5
\\\\
4x-y=1
\end{cases}\]

Answer 1

The second equation times 5 gives 20x−5y=5, which is the same as the first. So the equations are dependent and there are infinitely many solutions: all points on the line 4x−y=1, i.e. (x,y) = (t,4t−1) for any real t.