Systems Of Equations(: Geronimo's bakery is ordering from Carlo's Factory.They are ordering two types of desserts, original cheesecake and cupcakes. On their order they purchased 200 desserts for a total of $24.If the cheesecakes cost $16 and the cupcakes were $8.Then how many of each dessert did the bakery order? Variables:

x=Cupcakes

y=Cheesecakes System equations:

8x+16y=200

x+y=24 Elimination Method! Substitution Method! Graphing Method! 1-8x+16y=200

x+y=24

2- 8x+16y=200

(8) 8x+8y=192

8y=8

y=1 3- 8x+16(1)=200

8x+16=200

8x=184

x=23 Solution= (23,1) 1- 8x+16y=200 2- y=-x+24

x+y=24 3- 8x+16(-x+24)=200

8x-16x+384=200

-8x=-184

x=23 4- 8(23)+16y=200

184+16y=200

16y=16

y=1 Solution = (23,1) 1- 8x+16y=200

x+y=24 2. y=-.5x+12.5

y=-x+24 3. Graph it. Solve for Y.

Multiply second equation

by 8, then your X's will be the

be the same.Then solve for Y.

which ends up being Y=1. To find the X value, plug in what you got for Y.

And solve for X, Which is X=23. And that gives you a solution of .... You choose one equation to change to y= then you plug in that Y= (Y=-x+24) to the other equation (8x+16y=200). In this case it gives you that x=23. Plug in that X=23 to an equation. {8(23)+16y=200}.And solve for the other variable. Y=1. And the solution.. On the graphing method you change the two equation to Y=.Then you can put that into the calculator and it gives you the graph. You can also graph it by points, For example, in the first one you would start in 12.5(y axis) then go right the .5 and down one.And for the second one you would start at 24(y axis)then go right one and down one. The two lines would cross at (23,1), which is the solution. Liked Method:

I personally like the elimination method.Adding or subtracting equations and finding the value of the variables, and then plunging it to an equations to find the other variable is easier than the other methods, for me. Disliked Method:

The graphing method is the one I would say I loathe the most, because when changing the system equations to Y= equations I always get confused or put the Y & X wrong. And then when graphing it, if the X is a negative I think you are supposed to go down. This is why I don't really like this method because my lines don't really match at the end. Solution: (23,1) Geronimo's bakery order a total of 23 cupcakes(x) and 1 cheesecake(y) from Carlo's Factory.

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# Systems Of Equations project

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