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The substitute is in!. x=algebra. By: Drake Hudspeth 03/07/11 Math-03. The Problem.

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The substitute is in

The substitute is in!

x=algebra

By: Drake Hudspeth

03/07/11

Math-03


The problem
The Problem

  • The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold three senior citizen tickets and one child ticket for a total of 38$. The school took in 52$ on the second day by selling three senior citizen tickets and two child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

    Equations-

    3x+y=38

    3x+2y=52


Graphing
Graphing

  • Use Microsoft Excel.

  • Plot your point in cells B2 and C2-B8 and C8.

  • Use cell A1 to put x.

  • In A2-A8 put -5,-3,-1,0,1,3,and5.

  • Put your equation in cells B1 and C1.

  • Go to insert and choose graphs.

  • Pick the x and y graph.

    The reason that I do not recommend this system is because there is no way to go back and see why you missed the answer and because you must first solve for y.


Substitution
Substitution

  • Start with one equation. 3x+y=38

  • Subtract the x on both sides. 3x-3x+y=38-3x

  • You now use this y on the next equation. 3x+2(38-3x)=52

  • Distribute or multiply what is outside of the parenthesis with what is inside of it. 3x+76-6x=52

  • Combine like terms. -3x=-24

  • Divide the two terms that you have. X=8

  • Use x to solve for y. 3(8)+y=38

  • Distribute. 24+y=38

  • Subtract the integer on the left from the integer on the right.

    38-24=14

  • You now have y. y=14

  • So x=8 and y=14.

    I enjoy this method because it is accurate and there are many steps to see where you have made a mistake.


Elimination
Elimination

  • You must use both equations in the beginning. First subtract one integer from the other. (3x+2y=52)-(3x+y=38). You now have y=14.

  • Now plug y=14 into one equation. 3x+2(14)=52

  • Distribute. 3x+28=52

  • Subtract the integer on the left from the integer on the right. 52-28=24

  • You should now have 3x=24. Now divide. 24/3=8

  • y=14 and x=8

    This method is okay to use but it will not always be this simple.


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