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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAt a scrapbooking party, guests brought a certain number of photographs to use, based on how many pages they will be assembling. Brittany plans to assemble 55 small pages and 22 large pages and brought a total of 2424 photographs to use. Florence brought 44 photographs, which is enough to assemble 11 small page. Assuming that the number of photographs on a page remains constant, how many photographs fit on a small page and a large page?\newlineA small page can fit ____\_\_\_\_ photographs, and a large one can fit ____\_\_\_\_ photographs.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAt a scrapbooking party, guests brought a certain number of photographs to use, based on how many pages they will be assembling. Brittany plans to assemble 55 small pages and 22 large pages and brought a total of 2424 photographs to use. Florence brought 44 photographs, which is enough to assemble 11 small page. Assuming that the number of photographs on a page remains constant, how many photographs fit on a small page and a large page?\newlineA small page can fit ____\_\_\_\_ photographs, and a large one can fit ____\_\_\_\_ photographs.
  1. Define Variables: Let xx be the number of photographs that fit on a small page and yy be the number of photographs that fit on a large page. Brittany's equation is 5x+2y=245x + 2y = 24. Florence's equation is x=4x = 4.
  2. Write Equations: Write the system of equations:\newline11) 5x+2y=245x + 2y = 24\newline22) x=4x = 4
  3. Substitute xx: Substitute xx from the second equation into the first equation:\newline5(4)+2y=245(4) + 2y = 24
  4. Solve for y: Solve for y:\newline20+2y=2420 + 2y = 24\newline2y=24−202y = 24 - 20\newline2y=42y = 4\newliney=2y = 2
  5. Finalize Solution: We already know xx from the second equation, so x=4x = 4 and y=2y = 2.
  6. Check Solution: Check the solution by substituting xx and yy back into the original equations:\newline11) 5(4)+2(2)=245(4) + 2(2) = 24\newline22) 4=44 = 4

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