Question

What does it look like when a system of equations has no solution?

Answer 1

If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

For example, we have the system of linear equations:

`\begin{gathered} y\text{ =3x + 2} \\ y\text{ - 3x = 0} \end{gathered}`

When we attempt to solve the system:

Subtract equation 1 from 2:

`\begin{gathered} y\text{ - 3x -y = 0 -(3x+2)} \\ -3x\text{ = -3x - 2} \\ \text{Collect like terms} \\ -3x\text{ + 3x = -2} \\ 0\text{ = -2} \end{gathered}`

The result is false. Hence, there is no solution