A cup of skim milk has 10 more than half the calories of a cup of whole milk. a cup of whole milk has 40 more calories than a glass of apple juice. If someone consumed a cup of each of the three, they would have 370 calories. how many calories must be in each?

1) s= w/2+10
2) w=a+40 (or a=w-40)
3) a+s+w=370

rewriting 3)...






then we find the others:

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Solve: x+y+z=6, 2x-y+z=3, 3x-z=0}

from 3: 
z=3x 
1 plus 2: 
(2x-y+z)+(x+y+z)=3+6 
3x+2z=9 
3x+2(3x)=9 
9x=9 
x=1 
so z=3 
from 1: 
x+y+z=1+y+3=6 
y+4=6 
y=2 

Solution: (1,2,3) 


:)

solve each system by the substitution method. 1) 2x^2-y^2=6 2) y=x^2-3

 


 



 



so y=0 or y=2 



y=0: 

 


 

or 



 


y=2: 


or
 

solutions 

(-sqrt(3),0)
(sqrt(3),0)
(-sqrt(5),2)
(sqrt(5),2) 



:)

Use the elimination method to solve the system.

Solution:

 

becomes 
 

 
which means y=-1 

and so... 
 

and thus x=-1 

solution: (-1,-1)