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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineSparkles the Clown makes balloon animals for children at birthday parties. At Ava's party, he made 33 balloon poodles and 33 balloon giraffes, which used a total of 1515 balloons. For Emmy's party, he used 1111 balloons to make 11 balloon poodle and 33 balloon giraffes. How many balloons does each animal require?\newlineEach poodle requires _\_ balloons and each giraffe requires _\_ balloons.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineSparkles the Clown makes balloon animals for children at birthday parties. At Ava's party, he made 33 balloon poodles and 33 balloon giraffes, which used a total of 1515 balloons. For Emmy's party, he used 1111 balloons to make 11 balloon poodle and 33 balloon giraffes. How many balloons does each animal require?\newlineEach poodle requires _\_ balloons and each giraffe requires _\_ balloons.
  1. Define variables: Let's define the variables.\newlineLet xx be the number of balloons required for a poodle.\newlineLet yy be the number of balloons required for a giraffe.
  2. Write Ava's equation: Write the equation for Ava's party.\newline3x3x (balloons for poodles) + 3y3y (balloons for giraffes) = 1515 (total balloons used)\newline3x+3y=153x + 3y = 15
  3. Write Emmy's equation: Write the equation for Emmy's party.\newline1x1x (balloons for poodles) + 3y3y (balloons for giraffes) = 1111 (total balloons used)\newlinex+3y=11x + 3y = 11
  4. Eliminate variable xx: We have the system of equations:\newline3x+3y=153x + 3y = 15\newlinex+3y=11x + 3y = 11\newlineWhich variable should we eliminate?\newlineWe can eliminate xx by multiplying the second equation by −3-3 and adding it to the first equation.
  5. Multiply second equation: Multiply the second equation by −3-3.\newline−3(x+3y)=−3(11)-3(x + 3y) = -3(11)\newline−3x−9y=−33-3x - 9y = -33
  6. Add to eliminate x: Add the new equation to the first equation to eliminate x.\newline(3x+3y)+(−3x−9y)=15+(−33)(3x + 3y) + (-3x - 9y) = 15 + (-33)\newline3x−3x+3y−9y=15−333x - 3x + 3y - 9y = 15 - 33\newline0x−6y=−180x - 6y = -18\newline−6y=−18-6y = -18
  7. Solve for y: Solve for y.\newline−6y=−18-6y = -18\newliney=−18−6y = \frac{-18}{-6}\newliney=3y = 3
  8. Substitute yy into equation: Substitute yy back into the second original equation to solve for xx.x+3(3)=11x + 3(3) = 11x+9=11x + 9 = 11x=11−9x = 11 - 9x=2x = 2
  9. Final balloon count: We found:\newlinex=2x = 2\newliney=3y = 3\newlineWhat is the number of balloons required for each poodle and each giraffe?\newlineEach poodle requires 22 balloons and each giraffe requires 33 balloons.

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