SOLUTION: Solve by the addition method: 11x +2y = -1 2x +3y = 13

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Question 285: Solve by the addition method:

11x +2y = -1
2x +3y = 13
Found 2 solutions by whenindoubt, AnlytcPhil:
Answer by whenindoubt(13)   (Show Source): You can put this solution on YOUR website!
this is a multi variable linear equation. the best method is to find a way to elminate one of the variables


-3 (11x + 2y = -1 )
by distributing this -3 we can eliminate the y varible. this does not change the equation because we are distributing evenly by the same scalar. the new equation would be


-33x -6y = 3


now take
2 (2x + 3y = 13)
for the same purposes, the new equation would be


4x + 6y = 26
and now adding the two new equations together the y variable cancels and we get.
-29x=29
x= -1


then by placing x into either equation we get the y variable.
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Solve by the addition method:

	

 11x + 2y = -1

  2x + 3y = 13



To eliminate the x's, we multiply thru each equation by numbers that will

cause the new coefficients of x to become equal in absolute value but

opposite in sign.



The least common multiple of coefficients of x, 11 and 2, is 22.  Thus we

want to cause one of the coefficients of x to become +22 and the other -22.



To accomplish this we multiply the first equation thru by 2 and the second

equation by -11



  22x +  4y =   -2

 -22x - 33y = -143

 -----------------

 

 Adding these vertically:

       -29y = -145

          y = 5  

 ------------------------

  11x + 2y = -1

   2x + 3y = 13

The least common multiple of coefficients of y, 2 and 3, is 6.  Thus we

want to cause one of the coefficients of x to become +6 and the other -6.

To accomplish this we multiply the first equation thru by 3 and the second

equation by -2

  33x + 6y =  -3

  -4x - 6y = -26

 -----------------

 Adding these vertically:

  29x      = -29

         x = -1

So the solution is (-1,5)



Edwin 

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