Question

Determine if the following system of equations has no solutions, infinitely many solutions or one solutiony=x-4y=x-3

Answer 1

We are asked to find out if the following system of equations has no solutions, infinitely many solutions, or one solution.

`\begin{gathered} y=x-4\quad eq.1 \\ y=x-3\quad eq.2 \end{gathered}`

Subtract eq.2 from eq.1

As you can see, both the variables canceled out and we are left with 0 = -1 which is not correct mathematically.

This means that this system of the equations has no solution

These two equations are parallel and they do not intersect any point which means that there is no solution.