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

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Presentation transcript:

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= X= 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