# LINR 3 | Lesson 1 | Explore 3 (Nature of Solution in a System)

Without graphing determine whether the lines intersect.

1).   $$y = \frac{2}{3} x -1$$ and  $$y = \frac{3}{4} x – 4$$

2).   $$2x-4y=16$$ and $$y=0.5x + 4$$

3).  $$2x – y = 3$$ and $$x + 2y = 4$$

4).  $$2x + 4y = 2$$ and $$y = -\frac{1}{2} x + 1$$

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

5).  Find the solution to each of the systems in 1 – 4.

6).  How were the systems different/same?

7).  Determine a rule for determining the number of solution to a system.