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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 • Claire has $54 to buy CD’s and books. Each CD costs $9, and each book costs $6.she wants to buy 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. Substitution • One way to solve this problem is by the Substitution 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. Substitution (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. Substitution (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 • First you have to find (Y) for both of the equations. By subtracting (X) on both sides X+Y=7 -X -X Y=-X+7 9X+6Y=54 -9X -9X

  10. Graphing (part 2) • After getting (X) you have to divide any equation that has a number in front of (Y) by that number to get (Y) for that equation 6Y=-9X+54 6 6 6 Y=-9/6X+9

  11. Graphing (part 3) • Then once you have both equation you plug it into the graph and the point at which they cross (the solution) that is you answer. Witch is 4 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -4 -6 -8 -10 Solution

  12. All in all….. • I think that all of these methods are good but I have to say that the easiest (in my opinion) is Elimination. I think this is the best way to do this because there is a lot less steps there are into solving the equation.

  13. THE END

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