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How Do You Solve a Word Problem Using the Elimination by Subtraction Method?

Jason and Leo both went to a Florida Marlins game. Jason bought two seats in Section 100 and one seat in Section 300 and paid a total of $6. Leo bought two seat in Section 100 but sold one seat in Section 300 and ended up paying a total of $2. What are the prices for seats in Section 100 and Section 300?

Summary

  1. 'x' and 'y' are variables that represent the cost of seats in Section 100 and Section 300
  2. We need to make equations to determine the value of each variable, or the cost of each ticket
  3. By adding -2x-y=-6 to 2x-y=2, we'll eliminate x and be able to solve for y
  4. Plug y=2 into 2x+y=6 in order to solve for 'x'
  5. Plug y=2 into 2x-y=2 to check the solution for x
  6. We can write our solution as an ordered pair (x,y)=(2,2)

Notes

    1. Variables are letters that represent unknown values
    2. In this problem we need to find the cost of seats in Section 100 and Section 300, so it makes sense to pick variables to represent each section!
    1. Use the problem statement to generate equations containing 'x' and 'y'
    2. 'Bought 2 seats in Section 100' is written as '2•x'
    3. 'Bought a seat in Section 300' is written as '+y'
    4. 'Paid a total of $6" is written as '=6'
    5. 'Sold one seat in Section 300' is written as '-y'
    6. 'Paying a total fo $2' is written as '=2'
    1. To solve for y, it's convenient to combine the equations in a special way and eliminate 'x'
    2. There are many ways of solving a system of equations, and the links below show you multiple options for this particular system of equations
    1. To solve for y, we must eliminate x
    2. Multiply 2x+y=6 by -1 so x can be eliminated
    3. Multiplying an equation by -1 flips all of the signs!
    1. Adding the resulting equations cancels out 2x and leaves -2y by itself
    2. To isolate 'y' we need to divide both sides by -2
    1. To solve for x, we'll plug y into our first equation
    1. To solve for x, we'll plug y into our first equation
    2. Once y is plugged in, we have to get x by itself
    3. Use the Subtraction Property of Equality to subtract 2 from both sides and isolate 2x
    4. To isolate 'x' from '2x' we need to divide both sides by 2
    1. We can write our solution as an ordered pair (x,y)=(2,2)
    2. Since we have one solution to this system of equations, our system is 'consistent' and 'independent'