Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Sparkles the Clown makes balloon animals for children at birthday parties. At Ava's party, he made $3$ balloon poodles and $3$ balloon giraffes, which used a total of $15$ balloons. For Emmy's party, he used $11$ balloons to make $1$ balloon poodle and $3$ balloon giraffes. How many balloons does each animal require? $\newline$ Each poodle requires $\_$ balloons and each giraffe requires $\_$ balloons.

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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

Sparkles the Clown makes balloon animals for children at birthday parties. At Ava's party, he made

3

balloon poodles and

3

balloon giraffes, which used a total of

15

balloons. For Emmy's party, he used

11

balloons to make

1

balloon poodle and

3

balloon giraffes. How many balloons does each animal require?

\newline

Each poodle requires

\_

balloons and each giraffe requires

\_

balloons.

Define variables: Let's define the variables. $\newline$ Let $x$ be the number of balloons required for a poodle. $\newline$ Let $y$ be the number of balloons required for a giraffe.
Write Ava's equation: Write the equation for Ava's party. $\newline$ $3x$ (balloons for poodles) + $3y$ (balloons for giraffes) = $15$ (total balloons used) $\newline$ $3x + 3y = 15$
Write Emmy's equation: Write the equation for Emmy's party. $\newline$ $1x$ (balloons for poodles) + $3y$ (balloons for giraffes) = $11$ (total balloons used) $\newline$ $x + 3y = 11$
Eliminate variable $x$ : We have the system of equations: $\newline$ $3x + 3y = 15$ $\newline$ $x + 3y = 11$ $\newline$ Which variable should we eliminate? $\newline$ We can eliminate $x$ by multiplying the second equation by $-3$ and adding it to the first equation.
Multiply second equation: Multiply the second equation by $-3$ . $\newline$ $-3(x + 3y) = -3(11)$ $\newline$ $-3x - 9y = -33$
Add to eliminate x: Add the new equation to the first equation to eliminate x. $\newline$ $(3x + 3y) + (-3x - 9y) = 15 + (-33)$ $\newline$ $3x - 3x + 3y - 9y = 15 - 33$ $\newline$ $0x - 6y = -18$ $\newline$ $-6y = -18$
Solve for y: Solve for y. $\newline$ $-6y = -18$ $\newline$ $y = \frac{-18}{-6}$ $\newline$ $y = 3$
Substitute $y$ into equation: Substitute $y$ back into the second original equation to solve for $x$ . $x + 3(3) = 11$ $x + 9 = 11$ $x = 11 - 9$ $x = 2$
Final balloon count: We found: $\newline$ $x = 2$ $\newline$ $y = 3$ $\newline$ What is the number of balloons required for each poodle and each giraffe? $\newline$ Each poodle requires $2$ balloons and each giraffe requires $3$ balloons.