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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineTwo classmates got together over the weekend to do their assigned History reading. Ronald can read 11 page per minute, while Eve can read 22 pages per minute. When they met, Ronald had already read 4040 pages, and Eve had already gotten through 3939 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?\newlineRonald and Eve had each read _\_ pages after _\_ minutes.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineTwo classmates got together over the weekend to do their assigned History reading. Ronald can read 11 page per minute, while Eve can read 22 pages per minute. When they met, Ronald had already read 4040 pages, and Eve had already gotten through 3939 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?\newlineRonald and Eve had each read _\_ pages after _\_ minutes.
  1. Define Variables: Define the variables for the system of equations.\newlineLet xx represent the number of minutes they read together, and yy represent the total number of pages read by each person.
  2. Write Ronald's Equation: Write the equation for Ronald.\newlineRonald's reading rate is 11 page per minute, and he starts with 4040 pages already read. His equation is:\newliney=x+40y = x + 40
  3. Write Eve's Equation: Write the equation for Eve.\newlineEve's reading rate is 22 pages per minute, and she starts with 3939 pages already read. Her equation is:\newliney=2x+39y = 2x + 39
  4. Set Up System: Set up the system of equations.\newlineThe system of equations is:\newliney=x+40y = x + 40\newliney=2x+39y = 2x + 39
  5. Solve Using Substitution: Solve the system using substitution.\newlineSince both equations are equal to yy, set them equal to each other to find xx:\newlinex+40=2x+39x + 40 = 2x + 39
  6. Solve for x: Solve for x.\newlineSubtract xx from both sides of the equation:\newlinex+40−x=2x+39−xx + 40 - x = 2x + 39 - x\newline40=x+3940 = x + 39\newlineNow subtract 3939 from both sides:\newline40−39=x+39−3940 - 39 = x + 39 - 39\newline1=x1 = x
  7. Find y Value: Find the value of y by substituting x into one of the original equations.\newlineUsing Ronald's equation:\newliney=x+40y = x + 40\newliney=1+40y = 1 + 40\newliney=41y = 41
  8. Verify Solution: Verify the solution by substituting xx into Eve's equation.y=2x+39y = 2x + 39y=2(1)+39y = 2(1) + 39y=2+39y = 2 + 39y=41y = 41Since the value of yy is the same for both equations, the solution is correct.

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