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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineBrian and Eve are making presentations for a class project. Brian's slideshow starts with a verbal introduction that is 1313 seconds long, and then each slide is left up for 33 seconds. Eve leaves each slide onscreen for 44 seconds, and her introduction lasts 1111 seconds. Brian and Eve notice that their presentations have both the same number of slides and the same duration. How many slides are in each presentation? How long is each presentation?\newlineEach presentation has _\_ slides and is _\_ seconds long.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineBrian and Eve are making presentations for a class project. Brian's slideshow starts with a verbal introduction that is 1313 seconds long, and then each slide is left up for 33 seconds. Eve leaves each slide onscreen for 44 seconds, and her introduction lasts 1111 seconds. Brian and Eve notice that their presentations have both the same number of slides and the same duration. How many slides are in each presentation? How long is each presentation?\newlineEach presentation has _\_ slides and is _\_ seconds long.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of slides in each presentation.\newlineLet yy be the total duration of each presentation in seconds.\newlineNow we can write two equations based on the information given:\newlineFor Brian's presentation: y=13+3xy = 13 + 3x (1313 seconds for the introduction and 33 seconds for each slide)\newlineFor Eve's presentation: y=11+4xy = 11 + 4x (1111 seconds for the introduction and 44 seconds for each slide)\newlineSince both presentations have the same number of slides and the same duration, we can set the two equations equal to each other:\newline13+3x=11+4x13 + 3x = 11 + 4x
  2. Write Equations: Now we solve for xx: Subtract 3x3x from both sides: 13=11+x13 = 11 + x Subtract 1111 from both sides: 2=x2 = x So, x=2x = 2, which means there are 22 slides in each presentation.
  3. Set Equations Equal: Next, we substitute xx back into one of the original equations to find yy. We can use Brian's equation:\newliney=13+3xy = 13 + 3x\newliney=13+3(2)y = 13 + 3(2)\newliney=13+6y = 13 + 6\newliney=19y = 19\newlineSo, the total duration of each presentation is 1919 seconds.

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