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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEdwin and Keith decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Edwin went first and landed 11 arrow in the outer ring and 22 arrows in the bull's-eye, for a total of 218218 points. Keith went second and got 44 arrows in the outer ring and 22 arrows in the bull's-eye, earning a total of 290290 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 elimination, and fill in the blanks.\newlineEdwin and Keith decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Edwin went first and landed 11 arrow in the outer ring and 22 arrows in the bull's-eye, for a total of 218218 points. Keith went second and got 44 arrows in the outer ring and 22 arrows in the bull's-eye, earning a total of 290290 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. Write Equations: Let's denote the points for the outer ring as xx and the points for the bull's-eye as yy. We can write two equations based on the information given:\newlineEdwin's score: 1x+2y=2181x + 2y = 218\newlineKeith's score: 4x+2y=2904x + 2y = 290
  2. Eliminate Variables: To solve this system using elimination, we need to eliminate one of the variables. We can do this by subtracting Edwin's score from Keith's score:\newline(4x+2y)−(1x+2y)=290−218(4x + 2y) - (1x + 2y) = 290 - 218
  3. Simplify Equation: Simplifying the equation gives us: 3x=723x = 72
  4. Find Value of x: Now, we divide both sides by 33 to find the value of xx:x=723x = \frac{72}{3}x=24x = 24So, the outer ring is worth 2424 points.
  5. Substitute Value of x: With the value of x found, we can substitute it back into one of the original equations to find y. Let's use Edwin's score:\newline1x+2y=2181x + 2y = 218\newline24+2y=21824 + 2y = 218
  6. Isolate y Term: Subtract 2424 from both sides to isolate the term with yy: \newline2y=218−242y = 218 - 24\newline2y=1942y = 194
  7. Find Value of y: Now, divide both sides by 22 to find the value of y:\newliney=1942y = \frac{194}{2}\newliney=97y = 97\newlineSo, the bull's-eye is worth 9797 points.

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