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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineYesterday a chef used 4040 eggs to make 1010 chocolate souffles and 1010 lemon meringue pies. The day before, he made 22 chocolate souffles and 66 lemon meringue pies, which used 1616 eggs. How many eggs does each dessert require?\newlineA chocolate souffle requires _\_ eggs and a lemon meringue pie requires _\_ eggs.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineYesterday a chef used 4040 eggs to make 1010 chocolate souffles and 1010 lemon meringue pies. The day before, he made 22 chocolate souffles and 66 lemon meringue pies, which used 1616 eggs. How many eggs does each dessert require?\newlineA chocolate souffle requires _\_ eggs and a lemon meringue pie requires _\_ eggs.
  1. Define Variables: Let's define two variables: let xx be the number of eggs required for one chocolate souffle, and yy be the number of eggs required for one lemon meringue pie. We can then write two equations based on the information given:\newlineEquation 11 (from yesterday's production): 10x+10y=4010x + 10y = 40\newlineEquation 22 (from the day before yesterday's production): 2x+6y=162x + 6y = 16\newlineWe will use these equations to form a system of equations that we can solve using the elimination method.
  2. Form Equations: To use the elimination method, we want to eliminate one of the variables by making the coefficients of either xx or yy the same in both equations. We can multiply the entire second equation by 55 to match the coefficients of xx in the first equation:\newline5(2x+6y)=5(16)5(2x + 6y) = 5(16)\newline10x+30y=8010x + 30y = 80\newlineNow we have a new system of equations:\newline10x+10y=4010x + 10y = 40 (Equation 11)\newline10x+30y=8010x + 30y = 80 (New Equation 22)
  3. Elimination Method: Next, we subtract Equation 11 from the new Equation 22 to eliminate the xx variable:\newline(10x+30y)−(10x+10y)=80−40(10x + 30y) - (10x + 10y) = 80 - 40\newline10x+30y−10x−10y=80−4010x + 30y - 10x - 10y = 80 - 40\newline20y=4020y = 40\newlineNow we can solve for yy by dividing both sides by 2020:\newline20y20=4020\frac{20y}{20} = \frac{40}{20}\newliney=2y = 2\newlineSo, each lemon meringue pie requires 22 eggs.
  4. Substitute and Solve: Now that we have the value for yy, we can substitute it back into one of the original equations to solve for xx. We'll use Equation 11:\newline10x+10y=4010x + 10y = 40\newline10x+10(2)=4010x + 10(2) = 40\newline10x+20=4010x + 20 = 40\newlineSubtract 2020 from both sides to solve for xx:\newline10x=40−2010x = 40 - 20\newline10x=2010x = 20\newlineDivide both sides by 1010:\newlinexx00\newlinexx11\newlineSo, each chocolate souffle also requires xx22 eggs.

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