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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in 99 small candle holders and 1111 large candle holders, using a total of 9393 candles. On the west side, he replaced the candles in 1212 small candle holders and 1111 large candle holders, for a total of 102102 candles. How many candles does each candle holder hold?\newlineEach small candleholder holds _\_ candles, and each large one holds _\_ candles.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in 99 small candle holders and 1111 large candle holders, using a total of 9393 candles. On the west side, he replaced the candles in 1212 small candle holders and 1111 large candle holders, for a total of 102102 candles. How many candles does each candle holder hold?\newlineEach small candleholder holds _\_ candles, and each large one holds _\_ candles.
  1. Equation 11: Let's denote the number of candles a small candle holder holds as xx and the number of candles a large candle holder holds as yy. The volunteer replaced candles in 99 small candle holders and 1111 large candle holders on the east side, using a total of 9393 candles. This gives us our first equation:\newline9x+11y=939x + 11y = 93
  2. Equation 22: On the west side, the volunteer replaced the candles in 1212 small candle holders and 1111 large candle holders, for a total of 102102 candles. This gives us our second equation:\newline12x+11y=10212x + 11y = 102
  3. Solving System: We now have a system of equations:\newline9x+11y=939x + 11y = 93\newline12x+11y=10212x + 11y = 102\newlineTo solve the system, we can subtract the first equation from the second to eliminate yy.\newline(12x+11y)−(9x+11y)=102−93(12x + 11y) - (9x + 11y) = 102 - 93\newline12x+11y−9x−11y=912x + 11y - 9x - 11y = 9\newline3x=93x = 9\newlinex=3x = 3
  4. Substitute xx: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. Let's use the first equation:\newline9(3)+11y=939(3) + 11y = 93\newline27+11y=9327 + 11y = 93\newline11y=93−2711y = 93 - 27\newline11y=6611y = 66\newliney=6y = 6

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