 {{ 'mllessonnumberslides'  message : article.intro.bblockCount}} 
 {{ 'mllessonnumberexercises'  message : article.intro.exerciseCount}} 
 {{ 'mllessontimeestimation'  message }} 
The lines $ℓ_{1}$ and $ℓ_{2}$ are positioned as shown in the graph. Move the point $C$ vertically.
From the previous example, the following conclusions about systems of linear equations can be made.
Condition  Conclusion  Example 

The lines of the system have the same slope and the same $y$intercept.  The lines are coincidental. This means that there are infinitely many points of intersection. Therefore, the system has infinitely many solutions.  ${y=3x+1y=3x+1 $

The lines of the system have the same slope but different $y$intercept.  The lines are parallel. This means that there is not a point of intersection. Therefore, the system has no solution.  ${y=3x+1y=3x+5 $

The lines of the system have different slopes.  The lines are neither parallel nor coincidental. This means that there is one point of intersection. Therefore, the system has one solution.  ${y=3x+1y=2x+5 $

These conclusions can be seen in the following diagram.
In the previous graph, it can be seen that the initial angle between the lines measures $90_{∘}.$ Therefore, the lines are perpendicular.
The theorems seen in this lesson can be used to identify quadrilaterals and some of their properties.
Determine whether quadrilateral $ABCD$ is a parallelogram. Explain the reasoning.
Yes, see solution.
Recall that a parallelogram is a quadrilateral with two pairs of parallel sides.
Yes, see solution.
Start by drawing the diagonals of the rhombus. Then, find the slopes of the diagonals.