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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAndy loves riding Ferris wheels and roller coasters. While visiting the Morgan County Fair, he first went on the Ferris wheel 11 time, using a total of 22 tickets. Then, after taking a break and having a snack, Andy went on the Ferris wheel 22 times and the roller coaster 44 times, using a total of 2020 tickets. How many tickets does it take to ride each attraction?\newlineIt takes ____\_\_\_\_ tickets to ride the Ferris wheel, and ____\_\_\_\_ tickets to ride the roller coaster.

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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.\newlineAndy loves riding Ferris wheels and roller coasters. While visiting the Morgan County Fair, he first went on the Ferris wheel 11 time, using a total of 22 tickets. Then, after taking a break and having a snack, Andy went on the Ferris wheel 22 times and the roller coaster 44 times, using a total of 2020 tickets. How many tickets does it take to ride each attraction?\newlineIt takes ____\_\_\_\_ tickets to ride the Ferris wheel, and ____\_\_\_\_ tickets to ride the roller coaster.
  1. Define Variables: Let xx be the number of tickets for the Ferris wheel and yy be the number of tickets for the roller coaster. Andy's first ride gives the equation 1x+0y=21x + 0y = 2.
  2. Form Equations: Andy's second set of rides gives the equation 2x+4y=202x + 4y = 20.
  3. Create Augmented Matrix: Write the system of equations as an augmented matrix: [1amp;0amp;2 2amp;4amp;20]\left[\begin{array}{ccc} 1 & 0 & 2 \ 2 & 4 & 20 \end{array}\right].
  4. Eliminate Variable xx: Multiply the first row by −2-2 and add it to the second row to eliminate xx from the second equation: new second row is [0,4,16][0, 4, 16].
  5. Solve for y: Divide the second row by 44 to solve for yy: y=4y = 4.
  6. Solve for xx: Substitute y=4y = 4 into the first equation to solve for xx: 1x+0(4)=21x + 0(4) = 2, so x=2x = 2.
  7. Check Solution: Check the solution by substituting xx and yy into the second equation: 2(2)+4(4)=4+16=202(2) + 4(4) = 4 + 16 = 20, which is correct.

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