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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe receivers for the Seaside University football team are practicing running different routes on the field. They have to run a specific distance so that the quarterback knows exactly where to throw the ball. Damon ran 1818 post routes and 2929 slant routes, which meant he ran a total of 473473 yards. Porter ran 2828 post routes and 2929 slant routes, which equaled a total of 623623 yards. How long is each route?\newlineA post route is _\_ yards long and a slant route is _\_ yards long.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe receivers for the Seaside University football team are practicing running different routes on the field. They have to run a specific distance so that the quarterback knows exactly where to throw the ball. Damon ran 1818 post routes and 2929 slant routes, which meant he ran a total of 473473 yards. Porter ran 2828 post routes and 2929 slant routes, which equaled a total of 623623 yards. How long is each route?\newlineA post route is _\_ yards long and a slant route is _\_ yards long.
  1. Define Variables: Let's define two variables: let xx be the length of a post route in yards, and yy be the length of a slant route in yards. We can write two equations based on the information given:\newlineFor Damon: 18x+29y=47318x + 29y = 473 (11)\newlineFor Porter: 28x+29y=62328x + 29y = 623 (22)\newlineWe will use these equations to form a system of equations.
  2. Form System of Equations: To solve the system using elimination, we need to eliminate one of the variables. We can do this by subtracting equation (11) from equation (22) to eliminate yy:(28x+29y)−(18x+29y)=623−473(28x + 29y) - (18x + 29y) = 623 - 473This simplifies to:28x−18x=623−47328x - 18x = 623 - 473
  3. Elimination Method: Now we perform the subtraction:\newline10x=15010x = 150\newlineNext, we solve for xx by dividing both sides by 1010:\newlinex=15010x = \frac{150}{10}\newlinex=15x = 15\newlineSo, a post route is 1515 yards long.
  4. Solve for x: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. We'll use equation (11):18(15)+29y=47318(15) + 29y = 473270+29y=473270 + 29y = 473Now we subtract 270270 from both sides to solve for yy:29y=473−27029y = 473 - 27029y=20329y = 203
  5. Substitute xx into Equation: Finally, we divide both sides by 2929 to find the value of yy:y=20329y = \frac{203}{29}y=7y = 7So, a slant route is 77 yards long.

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