Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Students in a health class are tracking how much water they consume each day. Javier has two reusable water bottles: a small one and a large one. Yesterday, he drank $2$ small bottles and $1$ large bottle, for a total of $1,230$ grams. The day before, he drank $4$ small bottles and $3$ large bottles, for a total of $2,938$ grams. How much does each bottle hold? $\newline$ The small bottle holds $\_$ grams and the large one holds $\_$ grams.

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Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Students in a health class are tracking how much water they consume each day. Javier has two reusable water bottles: a small one and a large one. Yesterday, he drank

2

small bottles and

1

large bottle, for a total of

1,230

grams. The day before, he drank

4

small bottles and

3

large bottles, for a total of

2,938

grams. How much does each bottle hold?

\newline

The small bottle holds

\_

grams and the large one holds

\_

grams.

Define Equations: Let's denote the amount of grams the small bottle holds as $S$ and the large bottle as $L$ . We can then write two equations based on the given information.
First Day Consumption: The first equation comes from the first day's consumption: $2S + 1L = 1,230$ grams.
Second Day Consumption: The second equation comes from the second day's consumption: $4S + 3L = 2,938$ grams.
Elimination Method: To use elimination, we need to manipulate the equations so that when we add or subtract them, one of the variables is eliminated. Let's multiply the first equation by $3$ to align the $L$ terms. $\newline$ $3(2S + 1L) = 3(1,230)$ $\newline$ This gives us: $6S + 3L = 3,690$
New Equations: Now we have a system of two new equations: $\newline$ $6S + 3L = 3,690$ $\newline$ $4S + 3L = 2,938$
Eliminate Variable: Subtract the second equation from the first to eliminate $L$ : $(6S + 3L) - (4S + 3L) = 3,690 - 2,938$ This simplifies to: $2S = 752$
Solve for S: Now, divide both sides by $2$ to solve for S: $\newline$ $\frac{2S}{2} = \frac{752}{2}$ $\newline$ $S = 376$
Substitute for L: Now that we have the value for $S$ , we can substitute it back into one of the original equations to solve for $L$ . Let's use the first equation: $\newline$ $2(376) + L = 1,230$ $\newline$ $752 + L = 1,230$
Final Solution: Subtract $752$ from both sides to solve for $L$ : $\newline$ $L = 1,230 - 752$ $\newline$ $L = 478$