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. Melissa has two reusable water bottles: a small one and a large one. Yesterday, she drank $2$ small bottles and $4$ large bottles, for a total of $2,794$ grams. The day before, she drank $1$ small bottle and $4$ large bottles, for a total of $2,411$ 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. Melissa has two reusable water bottles: a small one and a large one. Yesterday, she drank

2

small bottles and

4

large bottles, for a total of

2,794

grams. The day before, she drank

1

small bottle and

4

large bottles, for a total of

2,411

grams. How much does each bottle hold?

\newline

The small bottle holds _____ grams and the large one holds _____ grams.

Set up equations: Let's denote the amount of grams the small bottle holds as $S$ and the large bottle as $L$ . We can set up two equations based on the given information: $\newline$ $1$ . For the first day: $2S + 4L = 2794$ grams $\newline$ $2$ . For the second day: $1S + 4L = 2411$ grams
Use elimination method: To use elimination, we can multiply the second equation by $2$ to align the coefficients of $S$ with the first equation: $\newline$ $2(1S + 4L) = 2 \times 2411$ $\newline$ This gives us: $2S + 8L = 4822$ grams
Subtract equations: Now we subtract the first equation from this new equation to eliminate $S$ : $(2S + 8L) - (2S + 4L) = 4822 - 2794$ This simplifies to: $4L = 2028$ grams
Solve for L: We can now solve for L by dividing both sides by $4$ : $\newline$ $\frac{4L}{4} = \frac{2028}{4}$ $\newline$ $L = 507$ grams
Substitute back and solve for S: With the value of L known, we can substitute it back into either of the original equations to solve for S. We'll use the second equation: $\newline$ $1S + 4(507) = 2411$ $\newline$ $S + 2028 = 2411$
Final solution: Subtract $2028$ from both sides to solve for $S$ : $\newline$ $S = 2411 - 2028$ $\newline$ $S = 383$ grams