The two lines represent two equations. Their intersection represents the point for which both equations are true. So A is the solution to the system.
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Let [tex]t[/tex] be the amount of time (minutes) used in a month on either plan. The first plan charges $0.18 for every minute, so you'd have to pay [tex]0.18t[/tex] each month. The second plan charges a flat fee of $49.95 plus $0.08 for every minute used, so that the total cost would be [tex]49.95+0.08t[/tex]. The second plan is preferable if its cost is less than the cost of the first plan. You want to find [tex]t[/tex] such that
[tex]0.18t=49.95+0.8t[/tex]
Solving gives
[tex]0.18t=49.95+0.8t\implies0.10t=49.95\implies t=499.5[/tex]
This means that after using 499.5 minutes, the second plan has a lower cost. (Just to check, if [tex]t=500[/tex], the first plan costs [tex]0.18(500)=90[/tex] while the second plan costs [tex]49.95+0.08(500)=89.95[/tex])
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Same idea as the previous problem. The daily cost for each mile [tex]m[/tex] with plan A is [tex]30+0.13m[/tex], while plan B has a fixed cost of $50, independent of [tex]m[/tex]. The plans cost the same when
[tex]30+0.13m=50\implies0.13m=20\implies m\approx153.8[/tex]
but plan B starts to save money for any mileage beyond that.
