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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineJulian and Lee went to an arcade where the machines took tokens. Julian played 44 games of skee ball and 33 games of pinball, using a total of 1717 tokens. At the same time, Lee played 11 game of pinball, using up 33 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires ____\_\_\_\_ tokens, and every game of pinball requires ____\_\_\_\_ tokens.

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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.\newlineJulian and Lee went to an arcade where the machines took tokens. Julian played 44 games of skee ball and 33 games of pinball, using a total of 1717 tokens. At the same time, Lee played 11 game of pinball, using up 33 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires ____\_\_\_\_ tokens, and every game of pinball requires ____\_\_\_\_ tokens.
  1. Define Variables: Let xx be the number of tokens required for a game of skee ball and yy for a game of pinball. Julian's games give us the equation 4x+3y=174x + 3y = 17.
  2. Julian's Equation: Lee's single game of pinball gives us the equation y=3y = 3.
  3. System of Equations: We now have the system of equations: 4x+3y=174x + 3y = 17 y=3y = 3
  4. Augmented Matrix: To solve using an augmented matrix, we write the coefficients of the variables and the constants in a matrix: [4amp;3amp;∣amp;17 0amp;1amp;∣amp;3]\begin{bmatrix} 4 & 3 & | & 17 \ 0 & 1 & | & 3 \end{bmatrix}
  5. Eliminate Variable: Since the second equation is already solved for yy, we can use it to eliminate yy from the first equation. We'll multiply the second row by −3-3 and add it to the first row.
  6. Multiply and Add: Multiplying the second row by −3-3 gives us:\newline[0−3∣−9][0 -3 | -9]
  7. Updated Matrix: Adding this to the first row:\newline[40∣8][4 0 | 8]
  8. Solve for xx: Now we have the matrix: [4amp;0amp;∣amp;8 0amp;1amp;∣amp;3]\begin{bmatrix} 4 & 0 & \vert & 8 \ 0 & 1 & \vert & 3 \end{bmatrix}
  9. Solve for y: From the first row of the matrix, we have 4x=84x = 8, which gives us x=2x = 2.
  10. Final Token Requirements: We already know y=3y = 3 from the second row of the matrix.
  11. Final Token Requirements: We already know y=3y = 3 from the second row of the matrix.So, every game of skee ball requires 22 tokens, and every game of pinball requires 33 tokens.

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