A system of equations is graphed on the coordinate plane.
1 answer:
Answer: Last option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
Given the first equation:
You can identify that:
And given the second equation:
You can identify that:
Then, since:
You can conclude that the lines are parallel.
By defintion, when the lines of a system of equations are parallel, the system has No solution and it is classified as "Inconsistent".
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We know that the first cyclist has traveled 24.2 km at a speed of 10 km/h. Lets use the equation 
to find the time of the first cyclist:
So, we know that she has traveled for 2.42 hours.
We also know that after she has traveled for 2.42 hours another<span> cyclist sets out in the same direction, so if </span>
represents the time of our first cyclist, <span>the time of our second cyclist will be </span>
.
Now we are going to use the equation
to relate the speeds and times of the two cyclist:
For the first one:
equation (1)
For the second one:
equation (2)
Replace (1) in (2)
The only thing left now is solve for:
We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.
So, we know that she has traveled for 2.42 hours.
We also know that after she has traveled for 2.42 hours another<span> cyclist sets out in the same direction, so if </span>
Now we are going to use the equation
For the first one:
For the second one:
Replace (1) in (2)
The only thing left now is solve for
We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.