Lines have the same slopes but different y-intercepts
Lines have the same slopes and y-intercepts
In our exercise, we want to write a system of linear equations that has no solution. To do this, we can write two lines that have the same slope but different y-intercepts.
y= 2x+ 1 & (I) y= 2x+ 4 & (II)
Now we will use a graph to make sure that our example system is correct. Let's plot points (0, 1) and (0, 3) that represent the y-intercepts of both equations.
Next we will use the slope to draw another point for each line. Since both lines have a slope of 2, we will start at the y-intercepts and then move 1 unit right and 2 units up.
Finally we will connect the points with smooth lines.
We can see that the lines are parallel, so they do not have any point of intersection. This confirms that there is no solution to our example system.
