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Systems of equations

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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  1. Systems of equations By Bradley lenaway

  2. Math is as easy as 1,2,3

  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.

  4. 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

  5. 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

  6. 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

  7. 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)

  8. 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

  9. Graphing

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