# Nature of Solution in a System

Without graphing determine whether the lines intersect.

- \(y = \frac{2}{3} x -1\) and \(y = \frac{3}{4} x – 4\)
- \(2x-4y=16\) and \(y=0.5x + 4\)
- \(2x – y = 3\) and \(x + 2y = 4\)
- \(2x + 4y = 2\) and \(y = -\frac{1}{2} x + 1\)

Go to DESMOS and graph the pairs https://www.desmos.com/calculator

- Find the solution to each of the systems in 1 – 4.
- How were the systems different/same?
- Determine a rule for determining the number of solution to a system.