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Solve each of the following systems of equations. Find all solutions.

a.



(b)

Your Response:

 Feb 8, 2018
 #1
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x + y  =  -1    subtract x from both sides ⇒  y    =  - 1 - x   (1)

3x  =  4 - 3y      (2)

 

Note that we can put (1)   into (2)...and we have that

 

 

3x  =    4  -  3 [ 1 - x ]     simplify

 

3x  =  4  - 3  + 3x     if we subtract  3x from both sides we have

 

0  =  4 -3

 

0  = 1    This is never true...so.....strangely.....we have no solutions  for x and y !!!

 

 

 

3x  - 4y  + 2  =  0

10 - 10 y   =  10y  - 15x

 

Divide the second equation through by 5  and we get

 

2 - 2y = 2y - 3x

 

Add 3x to both sides....subtract  2, 2y from both sides

 

3x - 4y   =  - 2    (1)

 

 

Subtract 2 from both sides of the first equation  and we have

 

3x - 4y   =  -2     (2)

 

Notice that the transformed equations are exactly the same......whenever this occurs, we have  infinite solutions for x and y  !!!!

 

One way to express this is to let x be "fixed"  and  solve any of the equations for y

 

So......

 

3x - 4y = -2 

 

3x + 2  = 4y

 

[ 3x + 2 ] / 4  = y

 

 

So....the solution set can be expressed as  {x , y }   =  { x , [3x + 2] / 4 }

 

 

 

 

 

cool cool cool

 Feb 8, 2018

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