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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. $\newline$ At 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 $5$ small pages and $2$ large pages and brought a total of $24$ photographs to use. Florence brought $4$ photographs, which is enough to assemble $1$ 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? $\newline$ A small page can fit $\_\_\_\_$ photographs, and a large one can fit $\_\_\_\_$ photographs.

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Solve a system of equations using substitution: word problems

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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.

\newline

At 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

5

small pages and

2

large pages and brought a total of

24

photographs to use. Florence brought

4

photographs, which is enough to assemble

1

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?

\newline

A small page can fit

\_\_\_\_

photographs, and a large one can fit

\_\_\_\_

photographs.

Define Variables: Let $x$ be the number of photographs that fit on a small page and $y$ be the number of photographs that fit on a large page. Brittany's equation is $5x + 2y = 24$ . Florence's equation is $x = 4$ .
Write Equations: Write the system of equations: $\newline$ $1$ ) $5x + 2y = 24$ $\newline$ $2$ ) $x = 4$
Substitute $x$ : Substitute $x$ from the second equation into the first equation: $\newline$ $5(4) + 2y = 24$
Solve for y: Solve for y: $\newline$ $20 + 2y = 24$ $\newline$ $2y = 24 - 20$ $\newline$ $2y = 4$ $\newline$ $y = 2$
Finalize Solution: We already know $x$ from the second equation, so $x = 4$ and $y = 2$ .
Check Solution: Check the solution by substituting $x$ and $y$ back into the original equations: $\newline$ $1$ ) $5(4) + 2(2) = 24$ $\newline$ $2$ ) $4 = 4$

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