Examples on linear combinations on systems of equations

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EXAMPLE #1
HOW TO SOLVE THE PROBLEM

X-4Y= -1
-3X+2Y=0

3X-4Y= -1

                               +   -3X+2Y=0
_____________
-2Y= -1
Y=1/2

NOW TO SOLVE FOR X

-3X+2Y=0
-3X+2(1/2)=0
-3X+1=0

X=1/3
 

( 1/3 , 1/2 )


 

   
 
 

* FIRST YOU SHOULD ADD THE 2 EQUATIONS

   * NEXT YOU SHOULD HAVE WHAT EITHER Y OR X EQUALS (WHICH EVER ONE DID NOT CANCEL OUT)

    * AFTER YOU HAVE GOTTEN WHAT THAT VARIABLE IS SUBSTITUTE IT IN WITH THE EQUATION WHERE IT WAS LIKE IF THE ANSWER FOR Y WAS 1/2 AND THE EQUATION WAS 3X+2Y=0 THEN YOU WOULD PUT THE 6 WHERE THE Y IS SO NOW YOUR EQUATION WOULD BE 3X+2(1/2)=0

   * NOW YOU SHOULD SOLVE AND GET YOUR ANSWER FOR X

   * NOW YOU SHOULD HAVE YOU X AND YOUR Y
 
 
 

 
EXAMPLE # 2 
HOW TO SOLVE THE PROBLEM

3X+3Y=15
2X+6Y=22

-2 (3X+3Y) = -2 (15)

-6X - 6Y= -30
2X+6Y=22
_______________
-4X      = -8
X       =2

NOW TO SOLVE FOR Y

2X+6Y=22
2(2)+6Y=22
4+6Y=22
Y=3


 
 
 
 
 		    * FIRST YOU SHOULD MAKE IT TO WHERE WHEN YOU ADD YOUR 2 EQUATIONS SOMETHING WILL CANCEL EITHER THE X OR THE Y SO THATS Y I ADDED THE -2 TO EACH SIDE SO THE Y'S WILL CANCEL

   * NEXT I GOT WHAT X EQUALED
  
   * NOW SOLVE FOR Y BY SUBSTITUTING IT INTO THE OTHER EQUAION WHERE THE Y WAS 

   * NOW YOU SHOULD SOVE THE PROBLEM AND GHET WHAT X AND Y EQUAL
 
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