Systems of equations

By Bradley lenaway

Math is as easy as 1,2,3

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

Graphing