Systems of equations
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Systems of equations. By Bradley lenaway. Math is as easy as 1,2,3. Question .

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Systems of equations

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Systems of equations

Systems of equations

By Bradley lenaway


Math is as easy as 1 2 3

Math is as easy as 1,2,3


Question

Question

  • Clair has $54 to buy CD’s and books. Each CD costs $9, and each book costs $6.she wants to by exactly 7 items. Write and solve a system of equations that could be used to determine the number of CD’s and the number of books Claire buys.


Substation

Substation

  • One way to solve this problem is by the substation method, I am going to use this method in this slide.

  • CD’s- X

  • Books- Y

  • First you have to solve for Y.

  • X+Y=7 (this is how many items she can buy.)

  • 9X+6Y=$54 (how much money she has.)

    X+Y=7

    -X

    Y=-X=7


Substation part 2

Substation (part 2)

  • After getting (Y) you have to plug it into the other problem where (Y) is.

  • Then you have to distribute it

    You get this

Y=(-X+7)

9X+6(-X+7)=54

this plugging in the (Y)

9X-6X+42=54


Substation part 3

Substation (part 3)

  • After getting (9X-6X+42=54) you then have to solve for (X)

  • First subtract 9X-6X

  • After doing that you have to move(42) by subtracting. Then divide (-3X) on both sides.

  • You should get (4)

9X-6X+42=54

-3x+42=54

-42 -42

-3X= 12

-3X -3X

X=4


Elimination

Elimination

  • You can also get the same answer by another method called Elimination.

  • First put your two equations one on top of another

  • After doing so you then have to cancel out (Y) or (X). in this case I'm going to cancel out (Y) by multiplying (-6) by the whole equation.

X+Y=7

9X+6Y=$54

-6(X+Y=7)


Elimination part 2

Elimination (part 2)

  • After multiplying (-6) you the have to subtract both equations

  • (-6Y) and (6Y) cancel out. So you get (3X=12)

  • You then divide both sides by (3X)

  • And you should get (4)

-6X-6Y=42

- 9X+6Y=54

3X=12

3X 3X

X=4


Graphing

Graphing


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