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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineLily and Jen decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Lily went first and landed 55 arrows in the outer ring and 55 arrows in the bull's-eye, for a total of 560560 points. Jen went second and got 22 arrows in the outer ring and 55 arrows in the bull's-eye, earning a total of 503503 points. How many points is each region of the target worth?\newlineThe outer ring is worth __\_\_ points, and the bull's-eye is worth __\_\_ points.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineLily and Jen decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Lily went first and landed 55 arrows in the outer ring and 55 arrows in the bull's-eye, for a total of 560560 points. Jen went second and got 22 arrows in the outer ring and 55 arrows in the bull's-eye, earning a total of 503503 points. How many points is each region of the target worth?\newlineThe outer ring is worth __\_\_ points, and the bull's-eye is worth __\_\_ points.
  1. Denote Points: Let's denote the points for the outer ring as xx and the points for the bull's-eye as yy. Lily's score can be represented by the equation 5x+5y=5605x + 5y = 560.
  2. Represent Scores: Jen's score can be represented by the equation 2x+5y=5032x + 5y = 503.
  3. System of Equations: We now have a system of equations:\newline5x+5y=5605x + 5y = 560\newline2x+5y=5032x + 5y = 503
  4. Eliminate Variables: To solve the system, we can subtract the second equation from the first to eliminate yy and solve for xx.
    (5x+5y)−(2x+5y)=560−503(5x + 5y) - (2x + 5y) = 560 - 503
    5x+5y−2x−5y=560−5035x + 5y - 2x - 5y = 560 - 503
    3x=573x = 57
    x=57/3x = 57 / 3
    x=19x = 19
  5. Solve for x: Now that we have the value of xx, we can substitute it back into one of the original equations to solve for yy. Let's use the second equation: 2x+5y=5032x + 5y = 503.\newline2(19)+5y=5032(19) + 5y = 503\newline38+5y=50338 + 5y = 503\newline5y=503−385y = 503 - 38\newline5y=4655y = 465\newliney=4655y = \frac{465}{5}\newliney=93y = 93

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