# Systems of equations - PowerPoint PPT Presentation

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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

### 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