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  Linear Equations:  
   3x - 5y = 13  
     x-2y=5  
 

 
   ORLANDO "EL-DUQUE" HERNANDEZ 
 
 
 
 

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1) 3x - 5y =13 the original problem  

2) -3 ( x-2y =5) multiply the problem by -3  

3) -3x + 6y =-15  

4) y= -2  

5) 3x- 5( -2) =13 plug in y into the equation 

6) 3x + 10 =13  subtract 10 from each side 
    -10      ;   -10 

7) 3x = 3  divide each side by 3 
     3     3 

8) x = 1  

9) the answer is (1, -2) 

 
word problem:  

One week a business sold 40 baseball cards, the yankee cards for $ 8.50 and the braves cards for $ 9.75 in all, $398.75 was taken in. How many of each kinda were sold? 

 

 8.50x + 9.75y = 398.75
  x + y = 45 
  x = -y + 45 plug x in to the original  equation 
  8.50 ( -y + 45) + 9.75 y = 398.75
  -8.50y + 382.50 + 9.75y = 398.75>
  1.25y + 382.50 = 398.75
  -382.50     &nnbsp;           - 382.50
 1.25y  =  16.25
 1.25          1.25
 y= 13 plug y into the original equation
 x+ 13 = 45 
 -13        -13
 x= 32