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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

By Bradley lenaway

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

- 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)

- 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)

- 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

- 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)

- 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

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