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Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).
This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:
They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).
In our case, we are asked to write an equation in order to create an independent consistent linear system.
Note: Consistent means that the system has a solution.
First, we graph the given equation:
There are many different equations that will form an independent consistent linear system with this equation.
We are going to choose the following line equation:
Because when we graph this equation next to the previous line:
We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.
Answer:
The unit rate of speed is 52.5 miles per hour
<em><u>Solution:</u></em>
Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21 hours and 15 minutes
We know that, 1 hour = 60 minutes
21 hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours
So they drive 1115.625 miles in 21.25 hours
To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken
unit rate of speed means miles driven in 1 hour
So the unit rate of speed is 52.5 miles per hour