examples of graphing systems of equations

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EXAMPLE # 1
HOW TO SOLVE THE PROBLEM
The sum of a certain number and a second number is 24.  The first number minus the second is 40.  Find the numbers. 

X+Y= 24
X-Y=40
2X=64
X=32

32+Y=24
Y=-8

(32,-8)

   * First you need to combine the two X's and eliminate the two Y's
   
   * This gives you what X equals
   
   * Now go back to the first equation and put what you got X equals in the place of the X and solve for Y

   *  Now you have your two points
   

EXAMPLE #2
HOW TO SOLVE THE PROBLEM
The diference between two numbers is 3.  Three times the smaller plus two times the larger is 31.  what are the numbers?

-3(X-Y=3)-3
3X+2Y=31
-3X+3Y=-9
3X+2Y=31
9Y=22
Y=4.4

X-4.4=3
X=7.4

(7.4, 4.4)

   * First set up your equation 

   * Now solve for Y
  
   * Once you get what Y equals substitute it in where the y is in the other equation and solve for X

   *  ONce you solve for X you should have you two points

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